{"text_format":"1","workbook":"xlsx","n_sheets":84,"sheets":["Topics","CellCharts","CellChartsAN","Mean","MeanAN","SorP","MeanPorS","Median","MedianAN","Mode","ModeAN","Mode(2)","Mode(2an)","Location","LocationAN","PER.EXC","PER.EXC (an)","PER.INC","PER.INC (an)","PER.Textbook","PER.Textbook (an)","PR","PR(an)","QUA.EXC","QUA.INC","QUA.Textbook","Quartile","Quartile (an)","LargeDataSet","LargeDataSet (an)","Rank","Rank (an)","BP(1)","BP(1an)","BP(2)","BP(2an)","BP(3)","BP(3an)","BP(4)","BP(4an)","Weighted Mean","Weighted Mean (an)","EstMeanGroupedData","EstMeanGroupedData (an)","Geomean","GeomeanAN","Trimmed Mean","Trimmed MeanAN","V(1)","V(1an)","V(2)","V(3)","V(3an)","V(4)","V(4an)","V(5)","VariabilityNotesxx","V(3xxxx)","V(4xxxx)","V(5xxxx)","V(6xxxx)","V(5an)","V(6)","V(6an)","CV","CV (an)","DS","DS (an)","Skew","SkewAN","z","z (an)","Chebyshev","Chebyshev (an)","Empirical Rule","Normal Distribution","Bell(1)","Bell(1an)","Bell(2)","Bell(2an)","Bell&Cheb","Bell&ChebAN","Outlier","Outlier (an)"],"not_rendered":{"charts":20,"images":22,"macros":1,"external_links":0,"defined_names":10,"comments":7,"pivot_tables":2},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Topics","index":0,"n_rows":33,"n_cols":2,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["Descriptive Statistics: Tabular, Graphical and Numerical summaries of data."]
[]
["Chapter 2: Descriptive Statistics: Tabular and Graphical summaries of data."]
[]
["Chapter 3: Descriptive Statistics: Numerical summaries of data."]
[]
["Descriptive Statistics: Numerical Measures"]
["Topic","Excel Feature"]
["Histogram Cell Chart","Conditional Formatting"]
["Mean","AVERAGE function"]
["Median","MEDAIN function"]
["Mode","MODE.SNGL or COUNTIF functions"]
["Percentiles","PERCENTILE.INC function and \"by hand method\""]
["Quartiles","QUARTILE.INC function and \"by hand method\""]
["PERCENTRANK function","PERCENTRANK.INC function"]
["RANK functions","RANK.AVE RANK.EQ function"]
["Rank and Percentile tool","Rank and Percentile tool"]
["Weighted Mean","Formula"]
["Geometric Mean","Formula and GEOMEAN function"]
["Trimmed Mean"]
["Range","Formula"]
["Interquartile Range","Formula"]
["Sample Variance","VAR.S function"]
["Sample Standard Deviation","STDEV.S function"]
["Coefficient of Variation","Formula"]
["Descriptive Statistics tool","Descriptive Statistics tool"]
["Distribution Shape `","SKEW function"]
["z-Scores","Formulas"]
["Chebyshev's Theorem","Formulas"]
["Empirical Rule","Formulas"]
["Detecting Outliers","Formulas"]
["Five Number Summary","Formulas"]
["Box Plot","Chart tool or by hand"]

{"sheet":"CellCharts","index":1,"n_rows":96,"n_cols":16,"rows_kept":96,"cut":false,"hidden":false,"merged":[]}
["Using Conditional Formatting to create a Type Of Horizontal Histogram - Visulizing Data",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Increment"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10]
["Stats Test Sample 1",null,"Lower","Upper","Frequency Sample 1",null,"Class","Horizontal Histogram","Frequency","Dot Plot","Stem","Leaf"]
[{"$f":"CHOOSE(RANDBETWEEN(1,10),RANDBETWEEN(0,100),RANDBETWEEN(10,100),RANDBETWEEN(20,100),RANDBETWEEN(30,95),RANDBETWEEN(30,90),RANDBETWEEN(35,85),RANDBETWEEN(40,80),RANDBETWEEN(50,75),RANDBETWEEN(50,75),RANDBETWEEN(60,85))","v":59},null,0,{"$f":"C4+$P$2","v":10},{"$f":"COUNTIFS($A$4:$A$96,\">=\"&C4,$A$4:$A$96,\"<\"&D4)","v":2},null,{"$f":"C4&\" <= Score < \"&D4","v":"0 <= Score < 10"},null,{"$f":"E4","v":2},{"$f":"REPT(\"*\",I4)","v":"**"},{"$f":"C4/10","v":0},{"$f":"REPT(\" 0 \",COUNTIF($A$4:$A$96,C4+0))&REPT(\" 1 \",COUNTIF($A$4:$A$96,C4+1))&REPT(\" 2 \",COUNTIF($A$4:$A$96,C4+2))&REPT(\" 3 \",COUNTIF($A$4:$A$96,C4+3))&REPT(\" 4 \",COUNTIF($A$4:$A$96,C4+4))&REPT(\" 5 \",COUNTIF($A$4:$A$96,C4+5))&REPT(\" 6 \",COUNTIF($A$4:$A$96,C4+6))&REPT(\" 7 \",COUNTIF($A$4:$A$96,C4+7))&REPT(\" 8 \",COUNTIF($A$4:$A$96,C4+8))&REPT(\" 9 \",COUNTIF($A$4:$A$96,C4+9))","v":" 2  5 "}]
[51,null,{"$f":"D4","v":10},{"$f":"C5+$P$2","v":20},3,null,{"$f":"C5&\" <= Score < \"&D5","v":"10 <= Score < 20"},null,3,"***",1,{"$f":"REPT(\" 0 \",COUNTIF($A$4:$A$96,C5+0))&REPT(\" 1 \",COUNTIF($A$4:$A$96,C5+1))&REPT(\" 2 \",COUNTIF($A$4:$A$96,C5+2))&REPT(\" 3 \",COUNTIF($A$4:$A$96,C5+3))&REPT(\" 4 \",COUNTIF($A$4:$A$96,C5+4))&REPT(\" 5 \",COUNTIF($A$4:$A$96,C5+5))&REPT(\" 6 \",COUNTIF($A$4:$A$96,C5+6))&REPT(\" 7 \",COUNTIF($A$4:$A$96,C5+7))&REPT(\" 8 \",COUNTIF($A$4:$A$96,C5+8))&REPT(\" 9 \",COUNTIF($A$4:$A$96,C5+9))","v":" 3  5  6 "}]
[50,null,{"$f":"D5","v":20},{"$f":"C6+$P$2","v":30},2,null,"20 <= Score < 30",null,2,"**",2," 6  7 "]
[70,null,30,40,4,null,"30 <= Score < 40",null,4,"****",3," 2  2  5  9 "]
[40,null,40,50,12,null,"40 <= Score < 50",null,12,"************",4," 0  2  2  4  4  6  6  6  7  8  8  9 "]
[70,null,50,60,17,null,"50 <= Score < 60",null,17,"*****************",5," 0  0  0  1  1  1  2  3  5  6  6  7  8  8  9  9  9 "]
[15,null,60,70,21,null,"60 <= Score < 70",null,21,"*********************",6," 0  0  0  0  1  1  1  2  2  3  3  3  5  7  7  7  7  8  9  9  9 "]
[42,null,70,80,22,null,"70 <= Score < 80",null,22,"**********************",7," 0  0  0  1  1  2  2  2  2  3  3  3  3  3  4  5  5  8  8  9  9  9 "]
[78,null,80,90,8,null,"80 <= Score < 90",null,8,"********",8," 0  1  2  4  4  4  9  9 "]
[62,null,90,100,2,null,"90 <= Score < 100",null,2,"**",9," 1  6 "]
[75,null,100,110,0,null,"100 <= Score < 110",null,0,"",10,""]
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[91]
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[{"$f":"CHOOSE(RANDBETWEEN(1,10),RANDBETWEEN(0,100),RANDBETWEEN(10,100),RANDBETWEEN(20,100),RANDBETWEEN(30,95),RANDBETWEEN(30,90),RANDBETWEEN(35,85),RANDBETWEEN(40,80),RANDBETWEEN(50,75),RANDBETWEEN(50,75),RANDBETWEEN(60,85))","v":70}]
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{"sheet":"CellChartsAN","index":2,"n_rows":96,"n_cols":16,"rows_kept":96,"cut":false,"hidden":false,"merged":[]}
["Using Conditional Formatting to create a Type Of Horizontal Histogram - Visulizing Data",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Increment"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10]
["Stats Test Sample 1",null,"Lower","Upper","Frequency Sample 1",null,"Class","Horizontal Histogram","Frequency","Dot Plot","Stem","Leaf"]
[{"$f":"CHOOSE(RANDBETWEEN(1,10),RANDBETWEEN(0,100),RANDBETWEEN(10,100),RANDBETWEEN(20,100),RANDBETWEEN(30,95),RANDBETWEEN(30,90),RANDBETWEEN(35,85),RANDBETWEEN(40,80),RANDBETWEEN(50,75),RANDBETWEEN(50,75),RANDBETWEEN(60,85))","v":57},null,0,{"$f":"C4+$P$2","v":10},{"$f":"COUNTIFS($A$4:$A$96,\">=\"&C4,$A$4:$A$96,\"<\"&D4)","v":0},null,{"$f":"C4&\" <= Score < \"&D4","v":"0 <= Score < 10"},{"$f":"E4","v":0},{"$f":"E4","v":0},{"$f":"REPT(\"*\",I4)","v":""},{"$f":"C4/10","v":0},{"$f":"REPT(\" 0 \",COUNTIF($A$4:$A$96,C4+0))&REPT(\" 1 \",COUNTIF($A$4:$A$96,C4+1))&REPT(\" 2 \",COUNTIF($A$4:$A$96,C4+2))&REPT(\" 3 \",COUNTIF($A$4:$A$96,C4+3))&REPT(\" 4 \",COUNTIF($A$4:$A$96,C4+4))&REPT(\" 5 \",COUNTIF($A$4:$A$96,C4+5))&REPT(\" 6 \",COUNTIF($A$4:$A$96,C4+6))&REPT(\" 7 \",COUNTIF($A$4:$A$96,C4+7))&REPT(\" 8 \",COUNTIF($A$4:$A$96,C4+8))&REPT(\" 9 \",COUNTIF($A$4:$A$96,C4+9))","v":""}]
[44,null,{"$f":"D4","v":10},{"$f":"C5+$P$2","v":20},4,null,{"$f":"C5&\" <= Score < \"&D5","v":"10 <= Score < 20"},4,4,"****",1,{"$f":"REPT(\" 0 \",COUNTIF($A$4:$A$96,C5+0))&REPT(\" 1 \",COUNTIF($A$4:$A$96,C5+1))&REPT(\" 2 \",COUNTIF($A$4:$A$96,C5+2))&REPT(\" 3 \",COUNTIF($A$4:$A$96,C5+3))&REPT(\" 4 \",COUNTIF($A$4:$A$96,C5+4))&REPT(\" 5 \",COUNTIF($A$4:$A$96,C5+5))&REPT(\" 6 \",COUNTIF($A$4:$A$96,C5+6))&REPT(\" 7 \",COUNTIF($A$4:$A$96,C5+7))&REPT(\" 8 \",COUNTIF($A$4:$A$96,C5+8))&REPT(\" 9 \",COUNTIF($A$4:$A$96,C5+9))","v":" 0  4  5  5 "}]
[79,null,{"$f":"D5","v":20},{"$f":"C6+$P$2","v":30},2,null,"20 <= Score < 30",2,2,"**",2," 3  5 "]
[62,null,30,40,1,null,"30 <= Score < 40",1,1,"*",3," 8 "]
[66,null,40,50,9,null,"40 <= Score < 50",9,9,"*********",4," 1  3  4  4  6  8  9  9  9 "]
[66,null,50,60,10,null,"50 <= Score < 60",10,10,"**********",5," 1  1  2  2  2  7  8  8  8  9 "]
[51,null,60,70,23,null,"60 <= Score < 70",23,23,"***********************",6," 0  0  1  2  2  4  4  4  4  5  5  6  6  6  6  6  6  6  7  7  8  8  9 "]
[71,null,70,80,22,null,"70 <= Score < 80",22,22,"**********************",7," 0  0  0  1  1  1  2  2  2  2  2  3  3  3  4  4  5  5  6  6  9  9 "]
[52,null,80,90,17,null,"80 <= Score < 90",17,17,"*****************",8," 0  0  1  1  1  2  2  3  3  4  5  5  5  5  6  7  8 "]
[76,null,90,100,5,null,"90 <= Score < 100",5,5,"*****",9," 0  3  4  5  7 "]
[75,null,100,110,0,null,"100 <= Score < 110",0,0,"",10,""]
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[49]
[10]
[72]
[59]
[81]
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[61]
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[72]
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[90]
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[81]
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[66]
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[74]
[94]
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[23]
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[25]
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[15]
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[58]
[79]
[46]
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{"sheet":"Mean","index":3,"n_rows":31,"n_cols":4,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["\"Typical Values\" calculated so that we have one value that can represent all the data points."]
[]
["Mean"]
["Arithmetic Mean: Add them up and divide by the count"]
["Good for quantitative data when there are not extreme values - extreme values can make the mean look too big or too small (Median more representative of a typical value in that case)"]
["Use AVERAGE function"]
[]
["Mean Test Scores",null,null,"Mean Weights (oz.)"]
[{"$f":"IF(B8<>\"\",\"We can use this average to compare to our scores and gage how well we did.\",\"\")","v":""},null,null,{"$f":"IF(E8<>\"\",\"We can use this average to help us estimate whether the machine is filling correctly.\",\"\")","v":""}]
[]
["Test Scores (Population)",null,null,"Weights (oz.) of Salad Bag from Filling Machine (Sample)"]
[60,null,null,10.8]
[68,null,null,10.74]
[76,null,null,10.32]
[84,null,null,9.73]
[55,null,null,9.15]
[63,null,null,10.94]
[89,null,null,10.83]
[31,null,null,9.36]
[47,null,null,10.42]
[68,null,null,9.9700000000000006]
[54,null,null,10.23]
[58,null,null,9.83]
[57,null,null,10.41]
[61,null,null,10.35]
[72,null,null,9.8699999999999992]
[91,null,null,10.02]
[95,null,null,9.4499999999999993]
[68,null,null,10.46]
[76,null,null,10.8]
[76,null,null,10.01]

{"sheet":"MeanAN","index":4,"n_rows":31,"n_cols":5,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["\"Typical Values\" calculated so that we have one value that can represent all the data points."]
[]
["Mean"]
["Arithmetic Mean: Add them up and divide by the count"]
["Good for quantitative data when there are not extreme values - extreme values can make the mean look too big or too small (Median more representative of a typical value in that case)"]
["Use AVERAGE function"]
[]
["Mean Test Scores",{"$f":"AVERAGE(A12:A31)","v":67.45},null,"Mean Weights (oz.)",{"$f":"AVERAGE(D12:D31)","v":10.184500000000002}]
[{"$f":"IF(B8<>\"\",\"We can use this average to compare to our scores and gage how well we did.\",\"\")","v":"We can use this average to compare to our scores and gage how well we did."},null,null,{"$f":"IF(E8<>\"\",\"We can use this average to help us estimate whether the machine is filling correctly.\",\"\")","v":"We can use this average to help us estimate whether the machine is filling correctly."}]
[]
["Test Scores (Population)",null,null,"Weights (oz.) of Salad Bag from Filling Machine (Sample)"]
[60,null,null,10.8]
[68,null,null,10.74]
[76,null,null,10.32]
[84,null,null,9.73]
[55,null,null,9.15]
[63,null,null,10.94]
[89,null,null,10.83]
[31,null,null,9.36]
[47,null,null,10.42]
[68,null,null,9.9700000000000006]
[54,null,null,10.23]
[58,null,null,9.83]
[57,null,null,10.41]
[61,null,null,10.35]
[72,null,null,9.8699999999999992]
[91,null,null,10.02]
[95,null,null,9.4499999999999993]
[68,null,null,10.46]
[76,null,null,10.8]
[76,null,null,10.01]

{"sheet":"SorP","index":5,"n_rows":5,"n_cols":1,"rows_kept":5,"cut":false,"hidden":false,"merged":[]}
["If the measures are computed for data from a sample, they are called sample statistics.\n"]
["If the measures are computed for data from a population, they are called population parameters.\n"]
["A sample statistic is referred to as the point estimator of the corresponding population parameter.\n"]
["Since it is usually impossible to get all the numbers for a population, we have to use sample statistics to reasonably estimate the population parameter!"]
["Example: calculate an sample average of number of salmon in Puget Sound and use it as the estimate of the population average of number of salmon in Puget Sound - \"We can't count all the fish in the sea!!\""]

{"sheet":"MeanPorS","index":6,"n_rows":18,"n_cols":5,"rows_kept":18,"cut":false,"hidden":false,"merged":[[12,3,17,4]]}
["Particular X","Popoulation Data",null,"Particular X","Sample Data"]
["X1",15,null,"X1",{"$f":"INDEX($B$2:$B$16,(ROWS(E$2:E2)-1)*2+1)","v":15}]
["X2",10,null,"X2",{"$f":"INDEX($B$2:$B$16,(ROWS(E$2:E3)-1)*2+1)","v":14}]
["X3",14,null,"X3",{"$f":"INDEX($B$2:$B$16,(ROWS(E$2:E4)-1)*2+1)","v":14}]
["X4",13,null,"X4",{"$f":"INDEX($B$2:$B$16,(ROWS(E$2:E5)-1)*2+1)","v":11}]
["X5",14,null,"X5",{"$f":"INDEX($B$2:$B$16,(ROWS(E$2:E6)-1)*2+1)","v":10}]
["X6",8,null,"X6",{"$f":"INDEX($B$2:$B$16,(ROWS(E$2:E7)-1)*2+1)","v":9}]
["X7",11,null,"X7",{"$f":"INDEX($B$2:$B$16,(ROWS(E$2:E8)-1)*2+1)","v":9}]
["X8",11,null,"X8",{"$f":"INDEX($B$2:$B$16,(ROWS(E$2:E9)-1)*2+1)","v":6}]
["X9",10]
["X10",13,null,"Xbar = ",{"$f":"AVERAGE(E2:E9)","v":11}]
["X11",9]
["X12",11,null,{"$f":"\"The Sample Statistic 'Sample Mean Xbar', \"&DOLLAR(E11)&\" is the point estimate of the Population Parameter 'Population Mean Mew'\"","v":"The Sample Statistic 'Sample Mean Xbar', $11.00 is the point estimate of the Population Parameter 'Population Mean Mew'"}]
["X13",9]
["X14",9]
["X15",6]
[]
["Mew = μ = ",{"$f":"AVERAGE(B2:B16)","v":10.866666666666667}]

{"sheet":"Median","index":7,"n_rows":33,"n_cols":11,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["\"Typical Values\" calculated so that we have one value that can represent all the data points."]
[]
["Median"]
["Sort, then take the one in the middle (odd count); average the middle two (even count)"]
["Good for quantitative data when there are extreme values (like house prices and salaries)"]
["Use MEDIAN function"]
[]
["Mean House Price",null,null,null,null,null,null,null,"Mean Salary"]
["Median House Price",null,null,null,null,null,null,null,"Median Salary"]
[{"$f":"IF(C9<>\"\",\"Median gives us a more representative 'typical value' to use in discussions and ads - because it is not affected by extreme values.\",\"\")","v":""},null,null,null,null,null,null,null,{"$f":"IF(K9<>\"\",\"Median gives us a more representative 'typical value' to make your decision. As soon as you see that the mean is larger than the median, you know that a few large values are pulling the mean up.\",\"\")","v":""}]
[]
["House Prices",null,"House Prices",null,null,null,null,null,"Salaries at Accounting Firm",null,"Salaries at Accounting Firm"]
[297873,null,297873,null,null,null,null,null,103332,null,103332]
[170143,null,170143,null,null,null,null,null,120102,null,120102]
[109159,null,109159,null,null,null,null,null,144354,null,144354]
[277309,null,277309,null,null,null,null,null,138409,null,138409]
[239136,null,239136,null,null,null,null,null,93949,null,93949]
[114460,null,114460,null,null,null,null,null,59915,null,59915]
[224649,null,224649,null,null,null,null,null,54594,null,54594]
[99857,null,99857,null,null,null,null,null,92784,null,92784]
[144686,null,144686,null,null,null,null,null,550250,null,550250]
[193308,null,193308,null,null,null,null,null,59196,null,59196]
[144244,null,144244,null,null,null,null,null,58072,null,58072]
[118492,null,118492,null,null,null,null,null,51671,null,51671]
[178708,null,178708,null,null,null,null,null,119001,null,119001]
[750022,null,750022,null,null,null,null,null,126737,null,126737]
[143400,null,143400,null,null,null,null,null,105127,null,105127]
[201661,null,201661,null,null,null,null,null,139330,null,139330]
[1258963,null,1258963,null,null,null,null,null,109151,null,109151]
[198345,null,198345,null,null,null,null,null,119831,null,119831]
[394136,null,394136,null,null,null,null,null,255800,null,255800]
[2589657,null,2589657,null,null,null,null,null,790500,null,790500]
[null,null,null,null,null,null,null,null,96842,null,96842]

{"sheet":"MedianAN","index":8,"n_rows":33,"n_cols":11,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["\"Typical Values\" calculated so that we have one value that can represent all the data points."]
[]
["Median"]
["Sort, then take the one in the middle (odd count); average the middle two (even count)"]
["Good for quantitative data when there are extreme values (like house prices and salaries)"]
["Use MEDIAN function"]
[]
["Mean House Price",null,{"$f":"AVERAGE(A13:A32)","v":392410.4},null,null,null,null,null,"Mean Salary",null,{"$f":"AVERAGE(I13:I33)","v":161378.42857142858}]
["Median House Price",null,{"$f":"MEDIAN(A13:A32)","v":195826.5},null,null,null,null,null,"Median Salary",null,{"$f":"MEDIAN(I13:I33)","v":109151}]
[{"$f":"IF(C9<>\"\",\"Median gives us a more representative 'typical value' to use in discussions and ads - because it is not affected by extreme values.\",\"\")","v":"Median gives us a more representative 'typical value' to use in discussions and ads - because it is not affected by extreme values."},null,null,null,null,null,null,null,{"$f":"IF(K9<>\"\",\"Median gives us a more representative 'typical value' to make your decision. As soon as you see that the mean is larger than the median, you know that a few large values are pulling the mean up.\",\"\")","v":"Median gives us a more representative 'typical value' to make your decision. As soon as you see that the mean is larger than the median, you know that a few large values are pulling the mean up."}]
[]
["House Prices",null,"House Prices",null,null,null,null,null,"Salaries at Accounting Firm",null,"Salaries at Accounting Firm"]
[297873,null,99857,null,null,null,null,null,103332,null,790500]
[170143,null,109159,null,null,null,null,null,120102,null,550250]
[109159,null,114460,null,null,null,null,null,144354,null,255800]
[277309,null,118492,null,null,null,null,null,138409,null,144354]
[239136,null,143400,null,null,null,null,null,93949,null,139330]
[114460,null,144244,null,null,null,null,null,59915,null,138409]
[224649,null,144686,null,null,null,null,null,54594,null,126737]
[99857,null,170143,null,null,null,null,null,92784,null,120102]
[144686,null,178708,null,null,null,null,null,550250,null,119831]
[193308,null,193308,null,null,null,null,null,59196,null,119001]
[144244,null,198345,null,null,null,null,null,58072,null,109151]
[118492,null,201661,null,null,null,null,null,51671,null,105127]
[178708,null,224649,null,null,null,null,null,119001,null,103332]
[750022,null,239136,null,null,null,null,null,126737,null,96842]
[143400,null,277309,null,null,null,null,null,105127,null,93949]
[201661,null,297873,null,null,null,null,null,139330,null,92784]
[1258963,null,394136,null,null,null,null,null,109151,null,59915]
[198345,null,750022,null,null,null,null,null,119831,null,59196]
[394136,null,1258963,null,null,null,null,null,255800,null,58072]
[2589657,null,2589657,null,null,null,null,null,790500,null,54594]
[null,null,null,null,null,null,null,null,96842,null,51671]

{"sheet":"Mode","index":9,"n_rows":35,"n_cols":6,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
["\"Typical Values\" calculated so that we have one value that can represent all the data points."]
[]
["Mode"]
["One that occurs most frequently (can be bimodal, multimodal)"]
["Good for Categorical Data (Nominal and Ordinal)"]
["Use MODE.SNGL for quantitative data and COUNTIF or PivotTable for Categorical or quantitative data."]
[]
["Rate Your Professor","Frequency"]
["Bad",null,"<< Mode is one that occurs most frequently"]
["Okay"]
["Good"]
["Great",null,null,"Mode For Test Data"]
[{"$f":"IF(AND(B9:B12<>\"\"),\"With Nominal or Ordinal Data we have a way of calculating a 'Typical Value'.\",\"\")","v":""},null,null,{"$f":"IF(E12<>\"\",\"MODE.SNGL will not tell you if there is more than one Mode. MODE.SNGL will just report the first one it encounters. A quick PivotTable will help reveal if there is more than one Mode.\",\"\")","v":""}]
[]
["Rate Your Professor",null,null,"Test Scores (Population)",null,"See this video for more about MODE.MULT"]
["Okay",null,null,60,null,"Excel Magic Trick 761: Formula Displaying Multiple Modes & Counting Modes Excel 2010 "]
["Good",null,null,68]
["Great",null,null,76]
["Bad",null,null,84]
["Bad",null,null,55]
["Bad",null,null,63]
["Bad",null,null,89]
["Good",null,null,31]
["Okay",null,null,47]
["Okay",null,null,68]
["Okay",null,null,54]
["Okay",null,null,58]
["Okay",null,null,57]
["Bad",null,null,61]
["Bad",null,null,72]
["Bad",null,null,91]
["Great",null,null,95]
["Good",null,null,68]
["Good",null,null,76]
["Bad",null,null,76]

{"sheet":"ModeAN","index":10,"n_rows":38,"n_cols":7,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
["\"Typical Values\" calculated so that we have one value that can represent all the data points."]
[]
["Mode"]
["One that occurs most frequently (can be bimodal, multimodal)"]
["Good for Categorical Data (Nominal and Ordinal)"]
["Use MODE.SNGL for quatitative data and COUNTIF or PivotTable for Categorical or quantitative data."]
[]
["Rate Your Professor","Frequency"]
["Bad",{"$f":"COUNTIF($A$19:$A$38,A9)","v":8},"<< Mode is one that occurs most frequently"]
["Okay",6]
["Good",4]
["Great",2,null,"Mode For Test Data",{"$f":"_xlfn.MODE.SNGL(D16:D35)","v":68}]
[{"$f":"IF(AND(B9:B12<>\"\"),\"With Nominal or Ordinal Data we have a way of calculating a 'Typical Value'.\",\"\")","v":"With Nominal or Ordinal Data we have a way of calculating a 'Typical Value'."},null,null,{"$f":"IF(E12<>\"\",\"MODE.SNGL will not tell you if there is more than one Mode. MODE.SNGL will just report the first one it encounters. A quick PivotTable will help reveal if there is more than one Mode.\",\"\")","v":"MODE.SNGL will not tell you if there is more than one Mode. MODE.SNGL will just report the first one it encounters. A quick PivotTable will help reveal if there is more than one Mode."}]
[]
["Single Array Formula for Retrieving Categorical Mode",null,null,"Test Scores (Population)",null,"See this video for more about MODE.MULT"]
[{"$f":"INDEX(A19:A38,_xlfn.MODE.SNGL(MATCH(A19:A38,A19:A38,0)))","v":"Bad"},null,null,60,null,"Excel Magic Trick 761: Formula Displaying Multiple Modes & Counting Modes Excel 2010 "]
[null,null,null,68]
["Rate Your Professor",null,null,76,null,"Test Scores (Population)","Frequency"]
["Okay",null,null,84,null,31,1]
["Good",null,null,55,null,47,1]
["Great",null,null,63,null,54,1]
["Bad",null,null,89,null,55,1]
["Bad",null,null,31,null,57,1]
["Bad",null,null,47,null,58,1]
["Bad",null,null,68,null,60,1]
["Good",null,null,54,null,61,1]
["Okay",null,null,58,null,63,1]
["Okay",null,null,57,null,68,3]
["Okay",null,null,61,null,72,1]
["Okay",null,null,72,null,76,3]
["Okay",null,null,91,null,84,1]
["Bad",null,null,95,null,89,1]
["Bad",null,null,68,null,91,1]
["Bad",null,null,76,null,95,1]
["Great",null,null,76,null,"Grand Total",20]
["Good"]
["Good"]
["Bad"]

{"sheet":"Mode(2)","index":11,"n_rows":245,"n_cols":12,"rows_kept":245,"cut":false,"hidden":false,"merged":[]}
["MODE function does no good for Categorical Data."]
["The Mode calculation is especially good for Categorical Data."]
["What is Microsoft thinking?"]
["To find Mode for categorical Data use: COUNTIF, PivotTable, Column Chart, or array formula"]
[]
[]
[]
["Lego Sets Sold During Christmas",null,"Lego Set","COUNTIF",null,null,null,null,null,null,null,"Lego Sets Sold During Christmas"]
["Kingdoms Set #7946 King's Castle",null,"2257 Ninjago Spinjitzu Starter Set",{"$f":"COUNTIF($A$9:$A$245,C9)","v":15},null,null,null,null,null,null,null,"Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089",null,"6166 Large Brick Box Building Blocks & Toys",41,null,null,null,null,null,null,null,"6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys",null,"City Exclusive Limited Edition Set #10211 Grand Emporium",30,null,null,null,null,null,null,null,"Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089",null,"Community Minifigure 256 Pcs (LG-9348)",16,null,null,null,null,null,null,null,"Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle",null,"Kingdoms Set #7946 King's Castle",77,null,null,null,null,null,null,null,"City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)",null,"Star War Hoth Wampa Set 8089",58,null,null,null,null,null,null,null,"2257 Ninjago Spinjitzu Starter Set"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys",null,"Array Formula for Cetegorical Data MODE:",null,null,null,null,null,null,null,null,{"$f":"INDEX($L$9:$L$14,RANDBETWEEN(RANDBETWEEN(1,3),RANDBETWEEN(4,6)))","v":"City Exclusive Limited Edition Set #10211 Grand Emporium"}]
["6166 Large Brick Box Building Blocks & Toys",null,"Mode"]
["2257 Ninjago Spinjitzu Starter Set",null,{"$f":"INDEX($A$9:$A$245,_xlfn.MODE.SNGL(MATCH($A$9:$A$245,$A$9:$A$245,0)))","v":"Kingdoms Set #7946 King's Castle"}]
["2257 Ninjago Spinjitzu Starter Set",null,"Count"]
["6166 Large Brick Box Building Blocks & Toys",null,{"$f":"COUNTIF($A$9:$A$245,C18)","v":77}]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set",null,"Data"]
["City Exclusive Limited Edition Set #10211 Grand Emporium",null,"6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium",null,"Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium",null,"Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set",null,"6166 Large Brick Box Building Blocks & Toys"]
["Community Minifigure 256 Pcs (LG-9348)",null,"Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089",null,"Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089",null,"Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089",null,"Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["2257 Ninjago Spinjitzu Starter Set"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Community Minifigure 256 Pcs (LG-9348)"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Community Minifigure 256 Pcs (LG-9348)"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
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["Community Minifigure 256 Pcs (LG-9348)"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["2257 Ninjago Spinjitzu Starter Set"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["2257 Ninjago Spinjitzu Starter Set"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]

{"sheet":"Mode(2an)","index":12,"n_rows":245,"n_cols":12,"rows_kept":245,"cut":false,"hidden":false,"merged":[]}
["MODE function does no good for Categorical Data."]
["The Mode calculation is especially good for Categorical Data."]
["What is Microsoft thinking?"]
["To find Mode for categorical Data use: COUNTIF, PivotTable, Column Chart, or array formula"]
[null,null,null,null,null,null,"Lego Sets Sold During Christmas","Frequency"]
[null,null,null,null,null,null,"2257 Ninjago Spinjitzu Starter Set",15]
[null,null,null,null,null,null,"6166 Large Brick Box Building Blocks & Toys",41]
["Lego Sets Sold During Christmas",null,"Lego Set","COUNTIF",null,null,"City Exclusive Limited Edition Set #10211 Grand Emporium",30,null,null,null,"Lego Sets Sold During Christmas"]
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["Star War Hoth Wampa Set 8089",null,"6166 Large Brick Box Building Blocks & Toys",41,null,null,"Kingdoms Set #7946 King's Castle",77,null,null,null,"6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys",null,"City Exclusive Limited Edition Set #10211 Grand Emporium",30,null,null,"Star War Hoth Wampa Set 8089",58,null,null,null,"Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089",null,"Community Minifigure 256 Pcs (LG-9348)",16,null,null,"Grand Total",237,null,null,null,"Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle",null,"Kingdoms Set #7946 King's Castle",77,null,null,null,null,null,null,null,"City Exclusive Limited Edition Set #10211 Grand Emporium"]
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["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys",null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($L$9:$L$14,RANDBETWEEN(RANDBETWEEN(1,3),RANDBETWEEN(4,6)))","v":"6166 Large Brick Box Building Blocks & Toys"}]
["6166 Large Brick Box Building Blocks & Toys"]
["2257 Ninjago Spinjitzu Starter Set"]
["2257 Ninjago Spinjitzu Starter Set"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys",null,"Array Formula for Cetegorical Data MODE:"]
["6166 Large Brick Box Building Blocks & Toys",null,"Mode"]
["6166 Large Brick Box Building Blocks & Toys",null,{"$f":"INDEX($A$9:$A$245,_xlfn.MODE.SNGL(MATCH($A$9:$A$245,$A$9:$A$245,0)))","v":"Kingdoms Set #7946 King's Castle"}]
["Kingdoms Set #7946 King's Castle",null,"Count"]
["6166 Large Brick Box Building Blocks & Toys",null,{"$f":"COUNTIF($A$9:$A$245,C35)","v":77}]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set",null,"Data"]
["City Exclusive Limited Edition Set #10211 Grand Emporium",null,"6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium",null,"Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium",null,"Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set",null,"6166 Large Brick Box Building Blocks & Toys"]
["Community Minifigure 256 Pcs (LG-9348)",null,"Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089",null,"Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089",null,"Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089",null,"Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["2257 Ninjago Spinjitzu Starter Set"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Community Minifigure 256 Pcs (LG-9348)"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Community Minifigure 256 Pcs (LG-9348)"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["2257 Ninjago Spinjitzu Starter Set"]
["Star War Hoth Wampa Set 8089"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["2257 Ninjago Spinjitzu Starter Set"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["2257 Ninjago Spinjitzu Starter Set"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["Community Minifigure 256 Pcs (LG-9348)"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["Star War Hoth Wampa Set 8089"]
["2257 Ninjago Spinjitzu Starter Set"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["Kingdoms Set #7946 King's Castle"]
["Kingdoms Set #7946 King's Castle"]
["6166 Large Brick Box Building Blocks & Toys"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Star War Hoth Wampa Set 8089"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]
["Kingdoms Set #7946 King's Castle"]
["City Exclusive Limited Edition Set #10211 Grand Emporium"]

{"sheet":"Location","index":13,"n_rows":36,"n_cols":10,"rows_kept":36,"cut":false,"hidden":false,"merged":[[21,9,22,9],[23,8,24,8],[23,9,24,9],[1,0,6,0],[7,0,12,0],[20,4,31,4],[21,6,32,6],[21,7,32,7],[21,8,22,8]]}
[null,"Measures of Location"]
["\"Typical Values\" calculated so that we have one value that can represent all the data points.","Mean","Arithmetic Mean: Add them up and divide by the count"]
[null,null,"Good for quantitative data when there are not extreme values - extreme values can make the mean look too big or too small (Medain more representative of a typical value in that case)"]
[null,"Median","Sort, then take the one in the middle (odd count); average the middle two (even count)"]
[null,null,"Good for quantitative data when there are extreme values (like house prices and salaries)"]
[null,"Mode","One that occurs most frequently (can be bimodal, multimodal)"]
[null,null,"Good for Nominal and Ordinal Data"]
["Markers in a sorted list that tell us what % of values are below and above.","Percentiles","For data sets without a lot of duplicates, Value Marking Point within a sorted list that says what % of values are less than or equal to the Value Marking Point. With Percentiles, we start with a decimal or percent and find the value (marking point)."]
[null,null,"Good for quantitative data"]
[null,null,"Example: CPA exam 70th Percentile is a score of 61 ==> 70% of the scores are less than or equal to 61 and 30% of the scores are equal to or greater than 61."]
[null,"Quartiles","Same as Percentiles but you divide the sorted list into 4 parts with 3 Value Marking Points. With Quartiles / Percentiles, we start with a decimal or percent and find the value (marking point)."]
[null,null,"For the CPA exam, the 1st, 2nd and 3rd quartiles (25%, 50% and 75% percentiles) are 45, 52 and 64, respectively. "]
[null,"PERCENTRANK function","Excel function that starts with the value (marking point) and finds the % of values below that marking point (opposite of what PERCENTILE.INC function does). To find the % of values above use 1 - PERCENTILE.INC function result."]
[null,null,"PERCENTILE.INC function counts the number of values below and divides that by the count - 1 (excludes itself from the total count). If the PERCENTILE.INC function looks at a value that is not in the list it interpolates  the value."]
[null,null,"Returns the rank of a value in a data set as a percentage of the data set. This function can be used to evaluate the relative standing of a value within a data set. For example, you can use PERCENTRANK.INC to evaluate the standing of an aptitude test score among all scores for the test."]
[]
[null,"Sample Data",null,"AVEARGE function","MEDIAN function","MODE.SNGL function","PERCENTILE.INC function","QUARTILE.INC function","PERCENTRANK.INC function"]
[null,16,null,"Quantitative Data","Quantitative Data","Categorical or Quatitative Data","Quantitative Data","Quantitative Data","Quantitative Data"]
[null,15,null,{"$f":"B2","v":"Mean"},{"$f":"B4","v":"Median"},{"$f":"B6","v":"Mode"},{"$f":"B8","v":"Percentiles"},{"$f":"B11","v":"Quartiles"}]
[null,14,null,null,null,null,0.75,3,14.25]
[null,11,null,null,{"$f":"IF(E20=\"\",\"\",TEXT(E34,\"0.00%\")&\" of the values are less than or equal to \"&DOLLAR(E20,2)&\" and \"&TEXT(E35,\"0.00%\")&\" of the values are greater than or equal to \"&DOLLAR(E20,2)&\".\")","v":""}]
[null,10,null,null,null,null,{"$f":"IF(G21=\"\",\"\",TEXT(G35,\"0.00%\")&\" of the values are less than or equal to \"&DOLLAR(G21,2)&\" and \"&TEXT(G36,\"0.00%\")&\" of the values are greater than or equal to \"&DOLLAR(G21,2)&\".\")","v":""},{"$f":"IF(H21=\"\",\"\",TEXT(H35,\"0.00%\")&\" of the values are less than or equal to \"&DOLLAR(H21,2)&\" and \"&TEXT(H36,\"0.00%\")&\" of the values are greater than or equal to \"&DOLLAR(H21,2)&\".\")","v":""},{"$f":"IF(I21=\"\",\"\",TEXT(I21,\"0.0%\")&\" below \"&DOLLAR(I20,2))","v":""},{"$f":"IF(J21=\"\",\"\",TEXT(J21,\"0.0%\")&\" above \"&DOLLAR(I20,2))","v":""}]
[null,9]
[null,9,null,null,null,null,null,null,"calculated with: 6/8","calculated with: 2/8"]
[null,6]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,0.5]
[null,null,null,null,{"$f":"1-E34","v":0.5},null,{"$f":"$G$20","v":0.75},{"$f":"$G$20","v":0.75}]
[null,null,null,null,null,null,{"$f":"1-G35","v":0.25},{"$f":"1-H35","v":0.25}]

{"sheet":"LocationAN","index":14,"n_rows":36,"n_cols":10,"rows_kept":36,"cut":false,"hidden":false,"merged":[[21,9,22,9],[23,8,24,8],[23,9,24,9],[1,0,6,0],[7,0,12,0],[20,4,31,4],[21,6,32,6],[21,7,32,7],[21,8,22,8]]}
[null,"Measures of Location"]
["\"Typical Values\" calculated so that we have one value that can represent all the data points.","Mean","Arithmetic Mean: Add them up and divide by the count"]
[null,null,"Good for quantitative data when there are not extreme values - extreme values can make the mean look too big or too small (Medain more representative of a typical value in that case)"]
[null,"Median","Sort, then take the one in the middle (odd count); average the middle two (even count)"]
[null,null,"Good for quantitative data when there are extreme values (like house prices and salaries)"]
[null,"Mode","One that occurs most frequently (can be bimodal, multimodal)"]
[null,null,"Good for Nominal and Ordinal Data"]
["Markers in a sorted list that tell us what % of values are below and above.","Percentiles","For data sets without a lot of duplicates, Value Marking Point within a sorted list that says what % of values are less than or equal to the Value Marking Point. With Percentiles, we start with a decimal or percent and find the value (marking point)."]
[null,null,"Good for quantitative data"]
[null,null,"Example: CPA exam 70th Percentile is a score of 61 ==> 70% of the scores are less than or equal to 61 and 30% of the scores are equal to or greater than 61."]
[null,"Quartiles","Same as Percentiles but you divide the sorted list into 4 parts with 3 Value Marking Points. With Quartiles / Percentiles, we start with a decimal or percent and find the value (marking point)."]
[null,null,"For the CPA exam, the 1st, 2nd and 3rd quartiles (25%, 50% and 75% percentiles) are 45, 52 and 64, respectively. "]
[null,"PERCENTRANK function","Excel function that starts with the value (marking point) and finds the % of values below that marking point (opposite of what PERCENTILE function does). To find the % of values above use 1 - PERCENTILE function result."]
[null,null,"PERCENTILE function counts the number of values below and divides that by the count - 1 (excludes itself from the total count). If the PERCENTILE function looks at a value that is not in the list it interpolates  the value."]
[null,null,"Returns the rank of a value in a data set as a percentage of the data set. This function can be used to evaluate the relative standing of a value within a data set. For example, you can use PERCENTRANK to evaluate the standing of an aptitude test score among all scores for the test."]
[]
[null,"Sample Data",null,"AVEARGE function","MEDIAN function","MODE.SNGL function","PERCENTILE.INC function","QUARTILE.INC function","PERCENTRANK.INC function"]
[null,16,null,"Quantitative Data","Quantitative Data","Categorical or Quatitative Data","Quantitative Data","Quantitative Data","Quantitative Data"]
[null,15,null,{"$f":"B2","v":"Mean"},{"$f":"B4","v":"Median"},{"$f":"B6","v":"Mode"},{"$f":"B8","v":"Percentiles"},{"$f":"B11","v":"Quartiles"}]
[null,14,null,{"$f":"AVERAGE(B18:B25)","v":11.25},{"$f":"MEDIAN(B18:B25)","v":10.5},{"$f":"_xlfn.MODE.SNGL(B18:B25)","v":9},0.75,3,14.25]
[null,11,null,null,{"$f":"IF(E20=\"\",\"\",TEXT(E34,\"0.00%\")&\" of the values are less than or equal to \"&DOLLAR(E20,2)&\" and \"&TEXT(E35,\"0.00%\")&\" of the values are greater than or equal to \"&DOLLAR(E20,2)&\".\")","v":"50.00% of the values are less than or equal to $10.50 and 50.00% of the values are greater than or equal to $10.50."},null,{"$f":"_xlfn.PERCENTILE.INC(B18:B25,G20)","v":14.25},{"$f":"_xlfn.QUARTILE.INC(B18:B25,H20)","v":14.25},{"$f":"_xlfn.PERCENTRANK.INC(B18:B25,I20)","v":0.75},{"$f":"1-I21","v":0.25}]
[null,10,null,null,null,null,{"$f":"IF(G21=\"\",\"\",TEXT(G35,\"0.00%\")&\" of the values are less than or equal to \"&DOLLAR(G21,2)&\" and \"&TEXT(G36,\"0.00%\")&\" of the values are greater than or equal to \"&DOLLAR(G21,2)&\".\")","v":"75.00% of the values are less than or equal to $14.25 and 25.00% of the values are greater than or equal to $14.25."},{"$f":"IF(H21=\"\",\"\",TEXT(H35,\"0.00%\")&\" of the values are less than or equal to \"&DOLLAR(H21,2)&\" and \"&TEXT(H36,\"0.00%\")&\" of the values are greater than or equal to \"&DOLLAR(H21,2)&\".\")","v":"75.00% of the values are less than or equal to $14.25 and 25.00% of the values are greater than or equal to $14.25."},{"$f":"IF(I21=\"\",\"\",TEXT(I21,\"0.0%\")&\" below \"&DOLLAR(I20,2))","v":"75.0% below $14.25"},{"$f":"IF(J21=\"\",\"\",TEXT(J21,\"0.0%\")&\" above \"&DOLLAR(I20,2))","v":"25.0% above $14.25"}]
[null,9]
[null,9,null,null,null,null,null,null,"calculated with: 6/8","calculated with: 2/8"]
[null,6]
[null,null,null,null,null,null,null,null,{"$f":"6/8","v":0.75},{"$f":"2/8","v":0.25}]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,0.5]
[null,null,null,null,{"$f":"1-E34","v":0.5},null,{"$f":"$G$20","v":0.75},{"$f":"$G$20","v":0.75}]
[null,null,null,null,null,null,{"$f":"1-G35","v":0.25},{"$f":"1-H35","v":0.25}]

{"sheet":"PER.EXC","index":15,"n_rows":15,"n_cols":8,"rows_kept":15,"cut":false,"hidden":false,"merged":[[13,3,14,3]]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 90.0% of the values are below the marking point, and 10.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.9,null,"PERCENTILE.EXC"]
[4,27,null,"Count = n =",null,null,1,"Can't use 0% or 100%"]
[5,30,null,"Position = (n+1)*p",null,null,2,"Position = (n+1)*p"]
[6,38,null,"How far between?"]
[7,39,null,"Distance between 2?"]
[8,42,null,"Amount to add to lower end"]
[9,43,null,{"$f":"\"Marking Point = \"&TEXT(E4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 90.00% Percentile"},null,{"$f":"\"Approximately \"&TEXT(E4,\"0.00%\")&\" of the CPA scores are below the score of \"&E10&\" and \"&TEXT(1-E4,\"0.00%\")&\" and above the score of \"&E10&\".\"","v":"Approximately 90.00% of the CPA scores are below the score of  and 10.00% and above the score of ."}]
[10,45,null,{"$f":"\"Marking Point = \"&TEXT(E4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 90.00% Percentile"},null,"PERCENTILE.EXC"]
[11,54]
[12,54,null,null,null,"Below",{"$f":"COUNT(B2:B14)/COUNT(B2:B15)","v":0.9285714285714286}]
[13,59,"13th","<< == Somewhere between these two.",null,"Above",{"$f":"COUNT(B15)/COUNT(B2:B15)","v":7.1428571428571425E-2}]
[14,97,"14th",null,null,"Total",{"$f":"SUM(G13:G14)","v":1}]

{"sheet":"PER.EXC (an)","index":16,"n_rows":15,"n_cols":8,"rows_kept":15,"cut":false,"hidden":false,"merged":[[13,3,14,3]]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 90.0% of the values are below the marking point, and 10.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.9,null,"PERCENTILE.EXC"]
[4,27,null,"Count = n =",{"$f":"COUNT(B2:B15)","v":14},null,1,"Can't use 0% or 100%"]
[5,30,null,"Position = (n+1)*p",{"$f":"(E5+1)*E4","v":13.5},null,2,"Position = (n+1)*p"]
[6,38,null,"How far between?",{"$f":"E6-INT(E6)","v":0.5}]
[7,39,null,"Distance between 2?",{"$f":"B15-B14","v":38}]
[8,42,null,"Amount to add to lower end",{"$f":"E8*E7","v":19}]
[9,43,null,{"$f":"\"Marking Point = \"&TEXT(E4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 90.00% Percentile"},{"$f":"B14+E9","v":78},{"$f":"\"Approximately \"&TEXT(E4,\"0.00%\")&\" of the CPA scores are below the score of \"&E10&\" and \"&TEXT(1-E4,\"0.00%\")&\" and above the score of \"&E10&\".\"","v":"Approximately 90.00% of the CPA scores are below the score of 78 and 10.00% and above the score of 78."}]
[10,45,null,{"$f":"\"Marking Point = \"&TEXT(E4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 90.00% Percentile"},{"$f":"_xlfn.PERCENTILE.EXC(B2:B15,E4)","v":78},"PERCENTILE.EXC"]
[11,54]
[12,54,null,null,null,"Below",{"$f":"COUNT(B2:B14)/COUNT(B2:B15)","v":0.9285714285714286}]
[13,59,"13th","<< == Somewhere between these two.",null,"Above",{"$f":"COUNT(B15)/COUNT(B2:B15)","v":7.1428571428571425E-2}]
[14,97,"14th",null,null,"Total",{"$f":"SUM(G13:G14)","v":1}]

{"sheet":"PER.INC","index":17,"n_rows":17,"n_cols":8,"rows_kept":17,"cut":false,"hidden":false,"merged":[[12,3,13,3]]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 90.0% of the values are below the marking point, and 10.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.9,null,"PERCENTILE.INC"]
[4,27,null,"Count = n =",null,null,1,"Can use 0% and 100%"]
[5,30,null,"Position = p*n+(1-p)",null,null,2,"Position = p*n+(1-p)"]
[6,38,null,"How far between?"]
[7,39,null,"Distance between 2?"]
[8,42,null,"Amount to add to lower end"]
[9,43,null,{"$f":"\"Marking Point = \"&TEXT($E$4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 90.00% Percentile"},null,{"$f":"\"Approximately \"&TEXT(E4,\"0.00%\")&\" of the CPA scores are below the score of \"&E10&\" and \"&TEXT(1-E4,\"0.00%\")&\" and below the score of \"&E10&\".\"","v":"Approximately 90.00% of the CPA scores are below the score of  and 10.00% and below the score of ."}]
[10,45,null,{"$f":"\"Marking Point = \"&TEXT($E$4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 90.00% Percentile"},null,"PERCENTILE.INC"]
[11,54,null,"Marking Point = 90.00% Percentile",null,"PERCENTILE"]
[12,54,"12th","<< == Somewhere between these two."]
[13,59,"13th"]
[14,97,null,null,null,"Below",{"$f":"COUNT(B2:B13)/COUNT(B2:B15)","v":0.8571428571428571}]
[null,null,null,null,null,"Above",{"$f":"COUNT(B14:B15)/COUNT(B2:B15)","v":0.14285714285714285}]
[null,null,null,null,null,"Total",{"$f":"SUM(G15:G16)","v":1}]

{"sheet":"PER.INC (an)","index":18,"n_rows":17,"n_cols":8,"rows_kept":17,"cut":false,"hidden":false,"merged":[[12,3,13,3]]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 90.0% of the values are below the marking point, and 10.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.9,null,"PERCENTILE.INC"]
[4,27,null,"Count = n =",{"$f":"COUNT(B2:B15)","v":14},null,1,"Can use 0% and 100%"]
[5,30,null,"Position = p*n+(1-p)",{"$f":"E4*E5+(1-E4)","v":12.7},null,2,"Position = p*n+(1-p)"]
[6,38,null,"How far between?",{"$f":"E6-INT(E6)","v":0.69999999999999929}]
[7,39,null,"Distance between 2?",{"$f":"B14-B13","v":5}]
[8,42,null,"Amount to add to lower end",{"$f":"E8*E7","v":3.4999999999999964}]
[9,43,null,{"$f":"\"Marking Point = \"&TEXT($E$4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 90.00% Percentile"},{"$f":"B13+E9","v":57.5},{"$f":"\"Approximately \"&TEXT(E4,\"0.00%\")&\" of the CPA scores are below the score of \"&E10&\" and \"&TEXT(1-E4,\"0.00%\")&\" and below the score of \"&E10&\".\"","v":"Approximately 90.00% of the CPA scores are below the score of 57.5 and 10.00% and below the score of 57.5."}]
[10,45,null,{"$f":"\"Marking Point = \"&TEXT($E$4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 90.00% Percentile"},{"$f":"_xlfn.PERCENTILE.INC(B2:B15,E4)","v":57.500000000000007},"PERCENTILE.INC"]
[11,54,null,"Marking Point = 90.00% Percentile",{"$f":"PERCENTILE(B2:B15,E4)","v":57.500000000000007},"PERCENTILE"]
[12,54,"12th","<< == Somewhere between these two."]
[13,59,"13th"]
[14,97,null,null,null,"Below",{"$f":"COUNT(B2:B13)/COUNT(B2:B15)","v":0.8571428571428571}]
[null,null,null,null,null,"Above",{"$f":"COUNT(B14:B15)/COUNT(B2:B15)","v":0.14285714285714285}]
[null,null,null,null,null,"Total",{"$f":"SUM(G15:G16)","v":1}]

{"sheet":"PER.Textbook","index":19,"n_rows":15,"n_cols":8,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 90.0% of the values are below the marking point, and 10.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.9,null,"Textbook: Percentile tells you the value in the sorted list that is a \"dividing line\" or \"marking point\" and marks that point at which approximately p% values lie blow marking point and (1-p%) values lie above marking point. If there are many duplicates, the approximation may be off a bit."]
[4,27,null,"Count = n =",null,null,"Step 1","Sort A to Z"]
[5,30,null,"Position = n*p",null,null,"Step 2","Compute Index = i = p*n\np = pth percentile as % (different than book)\nn = count of sample items\ni = tells you the position of the item in the sorted list"]
[6,38,null,"Percentile value",null,null,"Step 3","If i is not an integer, round up to the next position,\nif it is an integer, average i and i + 1."]
[7,39]
[8,42,null,"No function for this method",null,"textbook"]
[9,43,null,null,null,1,"Can use 0% and 100%"]
[10,45,null,null,null,2,"Position = n*p"]
[11,54]
[12,54,"12th",null,"Below",{"$f":"COUNT(B2:B13)/COUNT(B2:B15)","v":0.8571428571428571}]
[13,59,"13th",null,"Above",{"$f":"COUNT(B15)/COUNT(B2:B15)","v":7.1428571428571425E-2}]
[14,97,null,null,"Total",{"$f":"SUM(F13:F14)","v":0.92857142857142849}]

{"sheet":"PER.Textbook (an)","index":20,"n_rows":15,"n_cols":8,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 90.0% of the values are below the marking point, and 10.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.9,null,"Textbook: Percentile tells you the value in the sorted list that is a \"dividing line\" or \"marking point\" and marks that point at which approximately p% values lie blow marking point and (1-p%) values lie above marking point. If there are many duplicates, the approximation may be off a bit."]
[4,27,null,"Count = n =",{"$f":"COUNT(B2:B15)","v":14},null,"Step 1","Sort A to Z"]
[5,30,null,"Position = n*p",{"$f":"E5*E4","v":12.6},null,"Step 2","Compute Index = i = p*n\np = pth percentile as % (different than book)\nn = count of sample items\ni = tells you the position of the item in the sorted list"]
[6,38,null,"Percentile value",{"$f":"B14","v":59},null,"Step 3","If i is not an integer, round up to the next position,\nif it is an integer, average i and i + 1."]
[7,39]
[8,42,null,"No function for this method",null,"textbook"]
[9,43,null,null,null,1,"Can use 0% and 100%"]
[10,45,null,null,null,2,"Position = n*p"]
[11,54]
[12,54,"12th",null,"Below",{"$f":"COUNT(B2:B13)/COUNT(B2:B15)","v":0.8571428571428571}]
[13,59,"13th",null,"Above",{"$f":"COUNT(B15)/COUNT(B2:B15)","v":7.1428571428571425E-2}]
[14,97,null,null,"Total",{"$f":"SUM(F13:F14)","v":0.92857142857142849}]

{"sheet":"PR","index":21,"n_rows":15,"n_cols":6,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["No.","CPA Scores"]
[1,7,null,"PERCENTRANK.INC ==>> you give it the value and it will tell you the Percentile"]
[2,17]
[3,26,null,"Value",54]
[4,27,null,"Percentile",null,"PERCENTRANK.INC tells us the percentile"]
[5,30]
[6,38,null,{"$f":"IF(E5<>\"\",\"Approximately \"&TEXT(E5,\"0.00%\")&\" values below score of \"&E4&\" and \"&TEXT(1-E5,\"0.00%\")&\" values above.\",\"\")","v":""}]
[7,39]
[8,42]
[9,43]
[10,45]
[11,54]
[12,54]
[13,59]
[14,97]

{"sheet":"PR(an)","index":22,"n_rows":23,"n_cols":7,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["No.","CPA Scores"]
[1,7,null,"PERCENTRANK.INC ==>> you give it the value and it will tell you the Percentile"]
[2,17]
[3,26,null,"Value",54]
[4,27,null,"Percentile",{"$f":"_xlfn.PERCENTRANK.INC(B2:B15,E4)","v":0.76900000000000002},"PERCENTRANK.INC tells us the percentile"]
[5,30]
[6,38,null,{"$f":"IF(E5<>\"\",\"Approximately \"&TEXT(E5,\"0.00%\")&\" values below score of \"&E4&\" and \"&TEXT(1-E5,\"0.00%\")&\" values above.\",\"\")","v":"Approximately 76.90% values below score of 54 and 23.10% values above."}]
[7,39]
[8,42,null,"Point","Column1","Rank","Percent"]
[9,43,null,14,97,1,1]
[10,45,null,13,59,2,0.92300000000000004]
[11,54,null,11,54,3,0.76900000000000002]
[12,54,null,12,54,3,0.76900000000000002]
[13,59,null,10,45,5,0.69199999999999995]
[14,97,null,9,43,6,0.61499999999999999]
[null,null,null,8,42,7,0.53800000000000003]
[null,null,null,7,39,8,0.46100000000000002]
[null,null,null,6,38,9,0.38400000000000001]
[null,null,null,5,30,10,0.307]
[null,null,null,4,27,11,0.23]
[null,null,null,3,26,12,0.153]
[null,null,null,2,17,13,7.5999999999999998E-2]
[null,null,null,1,7,14,0]

{"sheet":"QUA.EXC","index":23,"n_rows":15,"n_cols":8,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 75.0% of the values are below the marking point, and 25.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.75,3]
[4,27,null,"Count = n =",{"$f":"COUNT(B2:B15)","v":14}]
[5,30,null,"Position = (n+1)*p",{"$f":"(E5+1)*E4","v":11.25},null,null,"QUARTILE.EXC"]
[6,38,null,"How far between?",{"$f":"E6-INT(E6)","v":0.25}]
[7,39,null,"Distance between 2?",{"$f":"B13-B12","v":0}]
[8,42,null,"Amount to add to lower end",{"$f":"E8*E7","v":0}]
[9,43,null,{"$f":"\"Marking Point = \"&TEXT(E4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 75.00% Percentile"},{"$f":"B12+E9","v":54},{"$f":"\"Approximately \"&TEXT(E4,\"0.00%\")&\" of the CPA scores are below the score of \"&E10&\" and \"&TEXT(1-E4,\"0.00%\")&\" and below the score of \"&E10&\".\"","v":"Approximately 75.00% of the CPA scores are below the score of 54 and 25.00% and below the score of 54."}]
[10,45,null,{"$f":"\"Marking Point = \"&TEXT(E4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 75.00% Percentile"},{"$f":"_xlfn.QUARTILE.EXC(B2:B15,F4)","v":54},"QUARTILE.EXC"]
[11,54]
[12,54,null,null,null,"Below",{"$f":"COUNT(B2:B11)/COUNT(B2:B15)","v":0.7142857142857143}]
[13,59,null,null,null,"Above",{"$f":"COUNT(B14:B15)/COUNT(B2:B15)","v":0.14285714285714285}]
[14,97]

{"sheet":"QUA.INC","index":24,"n_rows":16,"n_cols":7,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 75.0% of the values are below the marking point, and 25.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.75,3]
[4,27,null,"Count = n =",{"$f":"COUNT(B2:B15)","v":14}]
[5,30,null,"Position = p*n+(1-p)",{"$f":"E4*E5+(1-E4)","v":10.75}]
[6,38,null,"How far between?",{"$f":"E6-INT(E6)","v":0.75}]
[7,39,null,"Distance between 2?",{"$f":"B12-B11","v":9}]
[8,42,null,"Amount to add to lower end",{"$f":"E8*E7","v":6.75}]
[9,43,null,{"$f":"\"Marking Point = \"&TEXT($E$4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 75.00% Percentile"},{"$f":"B11+E9","v":51.75},{"$f":"\"Approximately \"&TEXT(E4,\"0.00%\")&\" of the CPA scores are below the score of \"&E10&\" and \"&TEXT(1-E4,\"0.00%\")&\" and below the score of \"&E10&\".\"","v":"Approximately 75.00% of the CPA scores are below the score of 51.75 and 25.00% and below the score of 51.75."}]
[10,45,null,{"$f":"\"Marking Point = \"&TEXT($E$4,\"0.00%\")&\" Percentile\"","v":"Marking Point = 75.00% Percentile"},{"$f":"_xlfn.QUARTILE.INC(B2:B15,F4)","v":51.75},"QUARTILE.INC"]
[11,54,null,"Marking Point = 75.00% Percentile",{"$f":"QUARTILE(B2:B15,F4)","v":51.75}]
[12,54]
[13,59]
[14,97,null,null,null,"Below",{"$f":"COUNT(B2:B11)/COUNT(B2:B15)","v":0.7142857142857143}]
[null,null,null,null,null,"Above",{"$f":"COUNT(B12:B15)/COUNT(B2:B15)","v":0.2857142857142857}]

{"sheet":"QUA.Textbook","index":25,"n_rows":15,"n_cols":8,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["No.","CPA Scores",null,"For data sets without a lot of duplicates, The pth percentile of a data set is a value such that at least p percent (decimal) of the items are less than or equal to this value and at least (1 - p) percent of the items are greater than or equal to this value."]
[1,7,null,{"$f":"\"Percentile:\"&CHAR(10)&\"We want to have a number from the sorted list that is the marking point that will say \"&TEXT(E4,\"0.0%\")&\" of the values are below the marking point, and \"&TEXT(1-E4,\"0.00%\")&\" of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'.\"","v":"Percentile:\nWe want to have a number from the sorted list that is the marking point that will say 75.0% of the values are below the marking point, and 25.00% of the values are above the marking point - a marking point that divided that data set into two parts. Percentile provides information about 'spread' and 'location'."}]
[2,17]
[3,26,null,"Percentile %",0.75,null,"Textbook: Percentile tells you the value in the sorted list that is a \"dividing line\" or \"marking point\" and marks that point at which approximately p% values lie blow marking point and (1-p%) values lie above marking point. If there are many duplicates, the approximation may be off a bit."]
[4,27,null,"Count = n =",{"$f":"COUNT(B2:B15)","v":14},null,"Step 1","Sort A to Z"]
[5,30,null,"Position = n*p",{"$f":"E5*E4","v":10.5},null,"Step 2","Compute Index = i = p*n\np = pth percentile as % (different than book)\nn = count of sample items\ni = tells you the position of the item in the sorted list"]
[6,38,null,"Percentile value",{"$f":"B12","v":54},null,"Step 3","If i is not an integer, round up to the next position,\nif it is an integer, average i and i + 1."]
[7,39]
[8,42,null,"No function for this method"]
[9,43]
[10,45]
[11,54]
[12,54,"12th",null,"Below",{"$f":"COUNT(B2:B11)/COUNT(B2:B15)","v":0.7142857142857143}]
[13,59,"13th",null,"Above",{"$f":"COUNT(B14:B15)/COUNT(B2:B15)","v":0.14285714285714285}]
[14,97]

{"sheet":"Quartile","index":26,"n_rows":17,"n_cols":9,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
[null,null,"Quartile divides data set in 4 parts with 3 markers"]
[null,null,"Percentile divided data set in 2 with 1 marker"]
["CPA Scores",null,"%","Quartile","QUARTILE.EXC","QUARTILE.INC",null,"PERCENTILE.EXC","PERCENTILE.INC"]
[7,null,0,0,null,null,null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C4)","v":{"$error":"#NUM!"}},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C4)","v":7}]
[17,null,0.25,1,null,null,null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C5)","v":26.75},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C5)","v":27.75}]
[26,null,0.5,2,null,null,null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C6)","v":40.5},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C6)","v":40.5}]
[27,null,0.75,3,null,null,null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C7)","v":54},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C7)","v":51.75}]
[30,null,1,4,null,null,null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C8)","v":{"$error":"#NUM!"}},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C8)","v":97}]
[38]
[39,null,null,"0 = MIN"]
[42,null,null,"1 = 1st Quartile"]
[43,null,null,"2 = 2nd Quartile"]
[45,null,null,"3 = 3rd Quartile"]
[54,null,null,"4 = MAX"]
[54]
[59]
[97]

{"sheet":"Quartile (an)","index":27,"n_rows":17,"n_cols":9,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
[null,null,"Quartile divides data set in 4 parts with 3 markers"]
[null,null,"Percentile divided data set in 2 with 1 marker"]
["CPA Scores",null,"%","Quartile","QUARTILE.EXC","QUARTILE.INC",null,"PERCENTILE.EXC","PERCENTILE.INC"]
[7,null,0,0,{"$f":"_xlfn.QUARTILE.EXC($A$4:$A$17,D4)","v":{"$error":"#NUM!"}},{"$f":"_xlfn.QUARTILE.INC($A$4:$A$17,D4)","v":7},null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C4)","v":{"$error":"#NUM!"}},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C4)","v":7}]
[17,null,0.25,1,{"$f":"_xlfn.QUARTILE.EXC($A$4:$A$17,D5)","v":26.75},{"$f":"_xlfn.QUARTILE.INC($A$4:$A$17,D5)","v":27.75},null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C5)","v":26.75},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C5)","v":27.75}]
[26,null,0.5,2,40.5,40.5,null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C6)","v":40.5},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C6)","v":40.5}]
[27,null,0.75,3,54,51.75,null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C7)","v":54},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C7)","v":51.75}]
[30,null,1,4,{"$error":"#NUM!"},97,null,{"$f":"_xlfn.PERCENTILE.EXC($A$4:$A$17,C8)","v":{"$error":"#NUM!"}},{"$f":"_xlfn.PERCENTILE.INC($A$4:$A$17,C8)","v":97}]
[38]
[39,null,null,"0 = MIN"]
[42,null,null,"1 = 1st Quartile"]
[43,null,null,"2 = 2nd Quartile"]
[45,null,null,"3 = 3rd Quartile"]
[54,null,null,"4 = MAX"]
[54]
[59]
[97]

{"sheet":"LargeDataSet","index":28,"n_rows":105,"n_cols":5,"rows_kept":105,"cut":false,"hidden":false,"merged":[]}
["Entrance Exam Scores",null,"Function","%","Result"]
[32,null,"PERCENTILE.EXC",0.75]
[43,null,"PERCENTILE.INC",0.75]
[86,null,"QUARTILE.EXC",3]
[63,null,"QUARTILE.INC",3]
[36,null,"PERCENTRANK.EXC",74]
[36,null,"PERCENTRANK.INC",74]
[52]
[88]
[51]
[89]
[44]
[39]
[10]
[74]
[82]
[20]
[14]
[43]
[10]
[41]
[44]
[86]
[89]
[78]
[30]
[8]
[13]
[4]
[38]
[83]
[70]
[37]
[69]
[86]
[63]
[23]
[20]
[23]
[61]
[60]
[93]
[75]
[29]
[11]
[29]
[2]
[25]
[94]
[73]
[56]
[6]
[33]
[27]
[64]
[5]
[72]
[87]
[2]
[33]
[48]
[12]
[57]
[42]
[41]
[89]
[63]
[26]
[78]
[86]
[60]
[34]
[7]
[39]
[10]
[94]
[47]
[71]
[29]
[16]
[72]
[45]
[1]
[10]
[81]
[51]
[78]
[20]
[32]
[60]
[82]
[64]
[77]
[68]
[43]
[8]
[83]
[15]
[79]
[65]
[74]
[2]
[78]
[3]
[76]

{"sheet":"LargeDataSet (an)","index":29,"n_rows":105,"n_cols":5,"rows_kept":105,"cut":false,"hidden":false,"merged":[]}
["Entrance Exam Scores",null,"Function","%","Result"]
[32,null,"PERCENTILE.EXC",0.75,{"$f":"_xlfn.PERCENTILE.EXC($A$2:$A$105,D2)","v":74}]
[43,null,"PERCENTILE.INC",0.75,{"$f":"_xlfn.PERCENTILE.INC($A$2:$A$105,D3)","v":74}]
[86,null,"QUARTILE.EXC",3,{"$f":"_xlfn.QUARTILE.EXC($A$2:$A$105,D4)","v":74}]
[63,null,"QUARTILE.INC",3,{"$f":"_xlfn.QUARTILE.INC($A$2:$A$105,D5)","v":74}]
[36,null,"PERCENTRANK.EXC",74,{"$f":"_xlfn.PERCENTRANK.EXC($A$2:$A$105,D6)","v":0.74199999999999999}]
[36,null,"PERCENTRANK.INC",74,{"$f":"_xlfn.PERCENTRANK.INC(A2:A105,D7)","v":0.747}]
[52]
[88]
[51]
[89]
[44]
[39]
[10]
[74]
[82]
[20]
[14]
[43]
[10]
[41]
[44]
[86]
[89]
[78]
[30]
[8]
[13]
[4]
[38]
[83]
[70]
[37]
[69]
[86]
[63]
[23]
[20]
[23]
[61]
[60]
[93]
[75]
[29]
[11]
[29]
[2]
[25]
[94]
[73]
[56]
[6]
[33]
[27]
[64]
[5]
[72]
[87]
[2]
[33]
[48]
[12]
[57]
[42]
[41]
[89]
[63]
[26]
[78]
[86]
[60]
[34]
[7]
[39]
[10]
[94]
[47]
[71]
[29]
[16]
[72]
[45]
[1]
[10]
[81]
[51]
[78]
[20]
[32]
[60]
[82]
[64]
[77]
[68]
[43]
[8]
[83]
[15]
[79]
[65]
[74]
[2]
[78]
[3]
[76]

{"sheet":"Rank","index":30,"n_rows":15,"n_cols":6,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Sales Reps","Sales","RANK.EQ","Percentile Rank",null,"RANK.AVE"]
["Sioux",57635]
["Chris",77866]
["Sue",72926]
["Phil",61073]
["Herb",76079]
["Tina",76363]
["Luong",72097]
["Fred",56871]
["Chin",74487]
["Choi",{"$f":"B10","v":74487}]
[]
["RANK.EQ deals with ties as equal, RANK.AVE deals with ties by averaging th epositional values; ex: (4+5)/2 = 4.5"]
["RANK.EQ or RANK.AVE function:\nref is all the values,\nnumber is the particular value to rank,\n0 = big to small (order)"]
["Screen shot of Rank & Percentile Excel tool:"]

{"sheet":"Rank (an)","index":31,"n_rows":15,"n_cols":6,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Sales Reps","Sales","RANK.EQ","Percentile Rank",null,"RANK.AVE"]
["Sioux",57635,{"$f":"_xlfn.RANK.EQ(B2,$B$2:$B$11,0)","v":9},{"$f":"_xlfn.PERCENTRANK.INC($B$2:$B$11,B2)","v":0.111},null,{"$f":"_xlfn.RANK.AVG(B2,$B$2:$B$11,0)","v":9}]
["Chris",77866,{"$f":"_xlfn.RANK.EQ(B3,$B$2:$B$11,0)","v":1},{"$f":"_xlfn.PERCENTRANK.INC($B$2:$B$11,B3)","v":1},null,{"$f":"_xlfn.RANK.AVG(B3,$B$2:$B$11,0)","v":1}]
["Sue",72926,6,0.44400000000000001,null,6]
["Phil",61073,8,0.222,null,8]
["Herb",76079,3,0.77700000000000002,null,3]
["Tina",76363,2,0.88800000000000001,null,2]
["Luong",72097,7,0.33300000000000002,null,7]
["Fred",56871,10,0,null,10]
["Chin",74487,4,0.55500000000000005,null,4.5]
["Choi",{"$f":"B10","v":74487},4,0.55500000000000005,null,4.5]
[]
["RANK.EQ deals with ties as equal, RANK.AVE deals with ties by averaging th epositional values; ex: (4+5)/2 = 4.5"]
["RANK.EQ or RANK.AVE function:\nref is all the values,\nnumber is the particular value to rank,\n0 = big to small (order)"]
["Screen shot of Rank & Percentile Excel tool:"]

{"sheet":"BP(1)","index":32,"n_rows":60,"n_cols":6,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
["Sample Data",null,"by hand",null,"position","Proportion"]
[15,null,"MIN",{"$f":"MIN(A2:A9)","v":15}]
[20,null,"Quartile1",{"$f":"AVERAGE(A3:A4)","v":22.5},{"$f":"COUNT($A$2:$A$9)*F3","v":2},0.25]
[25,null,"Quartile2",{"$f":"MEDIAN(A2:A9)","v":26}]
[25,null,"Quartile3",{"$f":"AVERAGE(A7:A8)","v":29},{"$f":"COUNT($A$2:$A$9)*F5","v":6},0.75]
[27,null,"MAX",{"$f":"MAX(A2:A9)","v":34}]
[28,null,"Interquartile Range",{"$f":"D5-D3","v":6.5}]
[30,null,"Lower Limit",{"$f":"D3-1.5*D7","v":12.75}," Quartile 1 - 1.5*Interquartile Range"]
[34,null,"Higher Limit",{"$f":"D5+1.5*D7","v":38.75},"Quartile 3 + 1.5*Interquartile Range"]
[null,null,"Smallest inside lower limit"]
[null,null,"Biggest inside lower limit"]
[]
[]
[]
[null,null,{"$f":"C2","v":"MIN"},{"$f":"D2-D1","v":15}]
[null,null,{"$f":"C3","v":"Quartile1"},{"$f":"D3-D2","v":7.5},"Neg Error Bar"]
[null,null,{"$f":"C4","v":"Quartile2"},{"$f":"D4-D3","v":3.5}]
[null,null,{"$f":"C5","v":"Quartile3"},{"$f":"D5-D4","v":3}]
[null,null,{"$f":"C6","v":"MAX"},{"$f":"D6-D5","v":5},"Pos Error Bar"]
[null,null,"Mean"]
[null,null,{"$f":"AVERAGE(A2:A9)","v":25.5},1]
[]
[]
[]
[]
[]
[]
[]
[null,null,{"$f":"C2&\" = \"&D2&CHAR(10)&C3&\" = \"&D3&CHAR(10)&C4&\" = \"&D4&CHAR(10)&C5&\" = \"&D5&CHAR(10)&C6&\" = \"&D6&CHAR(10)&C20&\" = \"&C21","v":"MIN = 15\nQuartile1 = 22.5\nQuartile2 = 26\nQuartile3 = 29\nMAX = 34\nMean = 25.5"}]
[]
[null,"Excel Box Plot Notes:"]
[null,1,"Calculate 5 number summary"]
[null,2,"Calculate the difference between each of the values: 1) Min - 0, 2) Q1 - MIN, 3) Q2 - Q1,  4) Q3 - Q3, 5) Max - Q3"]
[null,3,"Create Stacked Bar Chart"]
[null,4,"Switch Row and Column"]
[null,5,"Add fill = \"No Fill\" to 1st two parts of bar and last"]
[null,6,"Add Error Bar to 2nd part of bar with Minus / Custom / Negative = Quartile 1 - MIN"]
[null,7,"Add Error Bar to 4th part of bar with Plus / Custom / Positive = Max - Q3"]
[null,8,"Calculate Mean"]
[null,9,"Add Mean to Chart"]
[null,10,"Change that data point to X - Y Scatter"]
[null,11,"Edit Source data for X - Y Scatter and change X to Mean Value and Y to 1."]
[]
[]
[]
[]
[]
[]
[null,"or"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,6,"Add Error Bar 2nd part of bar as negative 100%"]
[null,7,"Add Error bar to 4th part with Positive Custom = Max - Q3"]

{"sheet":"BP(1an)","index":33,"n_rows":60,"n_cols":6,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
["Sample Data",null,"by hand",null,"position","Proportion"]
[15,null,"MIN",{"$f":"MIN(A2:A9)","v":15}]
[20,null,"Quartile1",{"$f":"AVERAGE(A3:A4)","v":22.5},{"$f":"COUNT($A$2:$A$9)*F3","v":2},0.25]
[25,null,"Quartile2",{"$f":"MEDIAN(A2:A9)","v":26}]
[25,null,"Quartile3",{"$f":"AVERAGE(A7:A8)","v":29},{"$f":"COUNT($A$2:$A$9)*F5","v":6},0.75]
[27,null,"MAX",{"$f":"MAX(A2:A9)","v":34}]
[28,null,"Interquartile Range",{"$f":"D5-D3","v":6.5}]
[30,null,"Lower Limit",{"$f":"D3-1.5*D7","v":12.75}," Quartile 1 - 1.5*Interquartile Range"]
[34,null,"Higher Limit",{"$f":"D5+1.5*D7","v":38.75},"Quartile 3 + 1.5*Interquartile Range"]
[null,null,"Smallest inside lower limit"]
[null,null,"Biggest inside lower limit"]
[]
[]
[]
[null,null,{"$f":"C2","v":"MIN"},{"$f":"D2-D1","v":15}]
[null,null,{"$f":"C3","v":"Quartile1"},{"$f":"D3-D2","v":7.5},"Neg Error Bar"]
[null,null,{"$f":"C4","v":"Quartile2"},{"$f":"D4-D3","v":3.5}]
[null,null,{"$f":"C5","v":"Quartile3"},{"$f":"D5-D4","v":3}]
[null,null,{"$f":"C6","v":"MAX"},{"$f":"D6-D5","v":5},"Pos Error Bar"]
[null,null,"Mean"]
[null,null,{"$f":"AVERAGE(A2:A9)","v":25.5},1]
[]
[]
[]
[]
[]
[]
[]
[null,null,{"$f":"C2&\" = \"&D2&CHAR(10)&C3&\" = \"&D3&CHAR(10)&C4&\" = \"&D4&CHAR(10)&C5&\" = \"&D5&CHAR(10)&C6&\" = \"&D6&CHAR(10)&C20&\" = \"&C21","v":"MIN = 15\nQuartile1 = 22.5\nQuartile2 = 26\nQuartile3 = 29\nMAX = 34\nMean = 25.5"}]
[]
[null,"Excel Box Plot Notes:"]
[null,1,"Calculate 5 number summary"]
[null,2,"Calculate the difference between each of the values: 1) Min - 0, 2) Q1 - MIN, 3) Q2 - Q1,  4) Q3 - Q3, 5) Max - Q3"]
[null,3,"Create Stacked Bar Chart"]
[null,4,"Switch Row and Column"]
[null,5,"Add fill = \"No Fill\" to 1st two parts of bar and last"]
[null,6,"Add Error Bar to 2nd part of bar with Minus / Custom / Negative = Quartile 1 - MIN"]
[null,7,"Add Error Bar to 4th part of bar with Plus / Custom / Positive = Max - Q3"]
[null,8,"Calculate Mean"]
[null,9,"Add Mean to Chart"]
[null,10,"Change that data point to X - Y Scatter"]
[null,11,"Edit Source data for X - Y Scatter and change X to Mean Value and Y to 1."]
[]
[]
[]
[]
[]
[]
[null,"or"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,6,"Add Error Bar 2nd part of bar as negative 100%"]
[null,7,"Add Error bar to 4th part with Positive Custom = Max - Q3"]

{"sheet":"BP(2)","index":34,"n_rows":33,"n_cols":13,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["Test Scores",null,null,null,null,null,null,null,"Lower Limit","Y",null,"Upper Limit","Y"]
[94,null,0,"MIN",null,null,null,null,{"$f":"$E$8","v":0},0,null,{"$f":"$E$9","v":0},0]
[55,null,1,"Quartile 1",null,null,null,null,0,1,null,0,1]
[72,null,2,"Quartile 2"]
[96,null,3,"Quartile 3"]
[74,null,4,"Max"]
[75,null,null,"Interquartile Range",null,"middle 50% of values"]
[28,null,null,"Lower Limit",null," Quartile 1 - 1.5*Interquartile Range"]
[40,null,null,"Upper Limit",null,"Quartile 3 + 1.5*Interquartile Range"]
[78,null,null,"Mean",null,1]
[65]
[67]
[54,null,null,"differences"]
[95,null,null,null,"Scores"]
[82,null,null,{"$f":"D2","v":"MIN"}]
[23,null,null,{"$f":"D3","v":"Quartile 1"}]
[70,null,null,{"$f":"D4","v":"Quartile 2"}]
[82,null,null,{"$f":"D5","v":"Quartile 3"}]
[34,null,null,{"$f":"D6","v":"Max"}]
[49]
[80,null,null,"Excel Box Plot Notes:"]
[null,null,null,1,"Calculate 5 number summary"]
[null,null,null,2,"Calculate the difference between each of the values: 1) Min - 0, 2) Q1 - MIN, 3) Q2 - Q1,  4) Q3 - Q3, 5) Max - Q3"]
[null,null,null,3,"Create Stacked Bar Chart"]
[null,null,null,4,"Switch Row and Column"]
[null,null,null,5,"Add fill = \"No Fill\" to 1st two parts of bar and last"]
[null,null,null,6,"Add Error Bar to 2nd part of bar with Minus / Custom / Negative = Quartile 1 - MIN"]
[null,null,null,7,"Add Error Bar to 4th part of bar with Plus / Custom / Positive = Max - Q3"]
[null,null,null,8,"Calculate Mean"]
[null,null,null,9,"Add Mean to Chart"]
[null,null,null,10,"Change that data point to X - Y Scatter"]
[null,null,null,11,"Edit Source data for X - Y Scatter and change X to Mean Value and Y to 1."]
[null,null,null,12,"Add Lower Limit and Upper Limit as X-Y Scatter Line."]

{"sheet":"BP(2an)","index":35,"n_rows":33,"n_cols":13,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["Test Scores",null,null,null,null,null,null,null,"Lower Limit","Y",null,"Upper Limit","Y"]
[94,null,0,"MIN",{"$f":"_xlfn.QUARTILE.INC($A$2:$A$21,C2)","v":23},null,null,null,{"$f":"$E$8","v":11.125},0,null,{"$f":"$E$9","v":122.125},0]
[55,null,1,"Quartile 1",{"$f":"_xlfn.QUARTILE.INC($A$2:$A$21,C3)","v":52.75},null,null,null,11.125,1,null,122.125,1]
[72,null,2,"Quartile 2",71]
[96,null,3,"Quartile 3",80.5]
[74,null,4,"Max",96]
[75,null,null,"Interquartile Range",{"$f":"E5-E3","v":27.75},"middle 50% of values"]
[28,null,null,"Lower Limit",{"$f":"E3-E7*1.5","v":11.125}," Quartile 1 - 1.5*Interquartile Range"]
[40,null,null,"Upper Limit",{"$f":"E5+E7*1.5","v":122.125},"Quartile 3 + 1.5*Interquartile Range"]
[78,null,null,"Mean",{"$f":"AVERAGE(A2:A21)","v":65.650000000000006},1]
[65]
[67]
[54,null,null,"differences"]
[95,null,null,null,"Scores"]
[82,null,null,{"$f":"D2","v":"MIN"},{"$f":"E2-E1","v":23}]
[23,null,null,{"$f":"D3","v":"Quartile 1"},{"$f":"E3-E2","v":29.75}]
[70,null,null,{"$f":"D4","v":"Quartile 2"},18.25]
[82,null,null,{"$f":"D5","v":"Quartile 3"},9.5]
[34,null,null,{"$f":"D6","v":"Max"},15.5]
[49]
[80,null,null,"Excel Box Plot Notes:"]
[null,null,null,1,"Calculate 5 number summary"]
[null,null,null,2,"Calculate the difference between each of the values: 1) Min - 0, 2) Q1 - MIN, 3) Q2 - Q1,  4) Q3 - Q3, 5) Max - Q3"]
[null,null,null,3,"Create Stacked Bar Chart"]
[null,null,null,4,"Switch Row and Column"]
[null,null,null,5,"Add fill = \"No Fill\" to 1st two parts of bar and last"]
[null,null,null,6,"Add Error Bar to 2nd part of bar with Minus / Custom / Negative = Quartile 1 - MIN"]
[null,null,null,7,"Add Error Bar to 4th part of bar with Plus / Custom / Positive = Max - Q3"]
[null,null,null,8,"Calculate Mean"]
[null,null,null,9,"Add Mean to Chart"]
[null,null,null,10,"Change that data point to X - Y Scatter"]
[null,null,null,11,"Edit Source data for X - Y Scatter and change X to Mean Value and Y to 1."]
[null,null,null,12,"Add Lower Limit and Upper Limit as X-Y Scatter Line."]

{"sheet":"BP(3)","index":36,"n_rows":398,"n_cols":7,"rows_kept":398,"cut":false,"hidden":false,"merged":[]}
["Differences to Determine Bar Lengths"]
[null,"CPA Scores 1","CPA Scores 2","CPA Scores 3","CPA Scores 4","CPA Scores 5"]
["Min"]
["Q1",null,null,null,null,null,"Neg. Errors Bar"]
["Q2"]
["Q3"]
["Max",null,null,null,null,null,"Pos. Errors Bar"]
[]
["Min",null,null,null,null,null,0]
["Q1",null,null,null,null,null,1]
["Q2",null,null,null,null,null,2]
["Q3",null,null,null,null,null,3]
["Max",null,null,null,null,null,4]
[]
[null,"CPA Scores 1","CPA Scores 2","CPA Scores 3","CPA Scores 4","CPA Scores 5"]
[null,{"$f":"CHOOSE(RANDBETWEEN(1,5),RANDBETWEEN(RANDBETWEEN(0,50),RANDBETWEEN(51,100)),RANDBETWEEN(RANDBETWEEN(30,50),RANDBETWEEN(51,70)),RANDBETWEEN(RANDBETWEEN(40,50),RANDBETWEEN(51,60)),RANDBETWEEN(RANDBETWEEN(30,70),RANDBETWEEN(71,85)),RANDBETWEEN(RANDBETWEEN(0,25),RANDBETWEEN(26,85)))","v":57},{"$f":"CHOOSE(RANDBETWEEN(1,5),RANDBETWEEN(RANDBETWEEN(0,50),RANDBETWEEN(51,100)),RANDBETWEEN(RANDBETWEEN(30,50),RANDBETWEEN(51,70)),RANDBETWEEN(RANDBETWEEN(40,50),RANDBETWEEN(51,60)),RANDBETWEEN(RANDBETWEEN(30,70),RANDBETWEEN(71,85)),RANDBETWEEN(RANDBETWEEN(0,25),RANDBETWEEN(26,85)))","v":68},63,51,77]
[null,{"$f":"CHOOSE(RANDBETWEEN(1,5),RANDBETWEEN(RANDBETWEEN(0,50),RANDBETWEEN(51,100)),RANDBETWEEN(RANDBETWEEN(30,50),RANDBETWEEN(51,70)),RANDBETWEEN(RANDBETWEEN(40,50),RANDBETWEEN(51,60)),RANDBETWEEN(RANDBETWEEN(30,70),RANDBETWEEN(71,85)),RANDBETWEEN(RANDBETWEEN(0,25),RANDBETWEEN(26,85)))","v":50},55,29,47,61]
[null,51,2,34,8,52]
[null,50,63,34,56,70]
[null,52,61,18,30,43]
[null,65,60,48,49,45]
[null,52,40,57,45,64]
[null,25,65,45,75,53]
[null,33,49,58,38,25]
[null,43,70,17,49,48]
[null,59,51,50,51,55]
[null,49,23,50,48,58]
[null,62,52,48,70,56]
[null,59,42,61,57,67]
[null,50,70,61,54,47]
[null,30,19,46,34,45]
[null,40,51,55,56,49]
[null,22,8,16,23,18]
[null,62,50,48,82,55]
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{"sheet":"BP(3an)","index":37,"n_rows":398,"n_cols":7,"rows_kept":398,"cut":false,"hidden":false,"merged":[]}
["Differences to Determine Bar Lengths"]
[null,"CPA Scores 1","CPA Scores 2","CPA Scores 3","CPA Scores 4","CPA Scores 5"]
["Min",{"$f":"B9-B8","v":3},{"$f":"C9-C8","v":3},5,2,4]
["Q1",{"$f":"B10-B9","v":40},41,35,41,39,"Neg. Errors Bar"]
["Q2",8,8,9,7,8]
["Q3",7,9,9.5,7.5,11]
["Max",28,30,28.5,33.5,27,"Pos. Errors Bar"]
[]
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["Q1",{"$f":"_xlfn.QUARTILE.INC(B$16:B$398,ROWS(B$9:B10)-1)","v":43},{"$f":"_xlfn.QUARTILE.INC(C$16:C$398,ROWS(C$9:C10)-1)","v":44},{"$f":"_xlfn.QUARTILE.INC(D$16:D$398,ROWS(D$9:D10)-1)","v":40},{"$f":"_xlfn.QUARTILE.INC(E$16:E$398,ROWS(E$9:E10)-1)","v":43},{"$f":"_xlfn.QUARTILE.INC(F$16:F$398,ROWS(F$9:F10)-1)","v":43}]
["Q2",{"$f":"_xlfn.QUARTILE.INC(B$16:B$398,ROWS(B$9:B11)-1)","v":51},{"$f":"_xlfn.QUARTILE.INC(C$16:C$398,ROWS(C$9:C11)-1)","v":52},{"$f":"_xlfn.QUARTILE.INC(D$16:D$398,ROWS(D$9:D11)-1)","v":49},{"$f":"_xlfn.QUARTILE.INC(E$16:E$398,ROWS(E$9:E11)-1)","v":50},{"$f":"_xlfn.QUARTILE.INC(F$16:F$398,ROWS(F$9:F11)-1)","v":51}]
["Q3",{"$f":"_xlfn.QUARTILE.INC(B$16:B$398,ROWS(B$9:B12)-1)","v":58},{"$f":"_xlfn.QUARTILE.INC(C$16:C$398,ROWS(C$9:C12)-1)","v":61},{"$f":"_xlfn.QUARTILE.INC(D$16:D$398,ROWS(D$9:D12)-1)","v":58.5},{"$f":"_xlfn.QUARTILE.INC(E$16:E$398,ROWS(E$9:E12)-1)","v":57.5},{"$f":"_xlfn.QUARTILE.INC(F$16:F$398,ROWS(F$9:F12)-1)","v":62}]
["Max",{"$f":"_xlfn.QUARTILE.INC(B$16:B$398,ROWS(B$9:B13)-1)","v":86},{"$f":"_xlfn.QUARTILE.INC(C$16:C$398,ROWS(C$9:C13)-1)","v":91},{"$f":"_xlfn.QUARTILE.INC(D$16:D$398,ROWS(D$9:D13)-1)","v":87},{"$f":"_xlfn.QUARTILE.INC(E$16:E$398,ROWS(E$9:E13)-1)","v":91},{"$f":"_xlfn.QUARTILE.INC(F$16:F$398,ROWS(F$9:F13)-1)","v":89}]
[]
[null,"CPA Scores 1","CPA Scores 2","CPA Scores 3","CPA Scores 4","CPA Scores 5"]
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[null,{"$f":"B7","v":"CPA Scores 1"},"CPA Scores 2","CPA Scores 3","CPA Scores 4","CPA Scores 5"]
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[26]

{"sheet":"Weighted Mean (an)","index":41,"n_rows":20,"n_cols":8,"rows_kept":20,"cut":false,"hidden":false,"merged":[]}
["Test Scores",null,{"$f":"A1","v":"Test Scores"},"Weight",{"$f":"D1&\"*\"&C1","v":"Weight*Test Scores"},null,"SUMPRODUCT: 1) Multiplies 2 columns, then 2) adds"]
[27,null,15,{"$f":"COUNTIF($A$2:$A$20,C2)","v":1},{"$f":"C2*D2","v":15},null,"Step 1:"]
[27,null,18,1,18,null,{"$f":"C2&\" * \"&D2&\" = \"","v":"15 * 1 = "},{"$f":"D2*C2","v":15}]
[15,null,19,1,19,null,"18 * 1 = ",{"$f":"D3*C3","v":18}]
[18,null,25,2,50,null,"19 * 1 = ",19]
[27,null,26,4,104,null,"25 * 2 = ",50]
[28,null,27,4,108,null,"26 * 4 = ",104]
[27,null,28,4,{"$f":"C8*D8","v":112},null,"27 * 4 = ",108]
[25,null,30,1,30,null,"28 * 4 = ",112]
[19,null,31,1,31,null,"30 * 1 = ",30]
[25,null,null,{"$f":"SUM(D2:D10)","v":19},{"$f":"SUM(E2:E10)","v":487},null,"31 * 1 = ",31]
[28]
[26,null,"Weighted Mean",{"$f":"E11/D11","v":25.631578947368421},null,null,"Step 2:",{"$f":"SUM(H3:H11)","v":487}]
[28,null,"Weighted Mean",{"$f":"SUMPRODUCT(C2:C10,D2:D10)/SUM(D2:D10)","v":25.631578947368421},"** SUMPRODUCT is specifically designed to multiply and then add two columns that are the same size."]
[26]
[28,null,"Mean From Original Data",{"$f":"AVERAGE(A2:A20)","v":25.631578947368421}]
[31]
[30]
[26]
[26]

{"sheet":"EstMeanGroupedData","index":42,"n_rows":201,"n_cols":16,"rows_kept":201,"cut":false,"hidden":false,"merged":[]}
["Age",null,null,null,"Quantitative: Integer, COUNTIFS",null,null,null,null,null,null,null,null,null,null,19]
[21,null,"Lower","Upper","Age","Frequency",null,"Midpoint",null,null,null,null,null,"Min"]
[57,null,0,{"$f":"C3+$P$1","v":19},{"$f":"C3&\" - \"&D3","v":"0 - 19"},{"$f":"COUNTIFS($A$2:$A$201,\">=\"&C3,$A$2:$A$201,\"<=\"&D3)","v":13},null,null,null,null,null,null,null,{"$f":"MIN($A$2:$A$201)","v":18}]
[25,null,{"$f":"D3+1","v":20},{"$f":"C4+$P$1","v":39},{"$f":"C4&\" - \"&D4","v":"20 - 39"},{"$f":"COUNTIFS($A$2:$A$201,\">=\"&C4,$A$2:$A$201,\"<=\"&D4)","v":110},null,null,null,null,null,null,null,"Max"]
[38,null,{"$f":"D4+1","v":40},{"$f":"C5+$P$1","v":59},{"$f":"C5&\" - \"&D5","v":"40 - 59"},{"$f":"COUNTIFS($A$2:$A$201,\">=\"&C5,$A$2:$A$201,\"<=\"&D5)","v":56},null,null,null,null,null,null,null,{"$f":"MAX($A$2:$A$201)","v":65}]
[22,null,{"$f":"D5+1","v":60},{"$f":"C6+$P$1","v":79},{"$f":"C6&\" - \"&D6","v":"60 - 79"},{"$f":"COUNTIFS($A$2:$A$201,\">=\"&C6,$A$2:$A$201,\"<=\"&D6)","v":21}]
[29,null,null,null,"Total",{"$f":"SUM(F3:F6)","v":200}]
[18]
[64,null,null,null,"Average Age",{"$f":"AVERAGE(A2:A201)","v":37.08}]
[27]
[22,null,null,null,"Average Age from Grouped Data"]
[39,null,null,null,"** will not be the same as actual mean because we are"]
[61,null,null,null,"estimating the data points when we use midpoint for the"]
[18,null,null,null,"unknown data points"]
[22]
[52]
[22]
[18]
[55]
[20]
[42]
[30]
[64]
[63]
[41]
[21]
[63]
[54]
[18]
[26]
[59]
[30]
[64]
[30]
[41]
[23]
[52]
[18]
[32]
[22]
[29]
[25]
[63]
[26]
[31]
[23]
[42]
[28]
[23]
[19]
[37]
[38]
[50]
[26]
[33]
[59]
[32]
[27]
[54]
[63]
[48]
[29]
[38]
[24]
[51]
[25]
[65]
[35]
[35]
[21]
[47]
[62]
[63]
[23]
[59]
[48]
[57]
[19]
[48]
[21]
[40]
[25]
[59]
[57]
[56]
[19]
[54]
[65]
[25]
[30]
[57]
[43]
[44]
[21]
[20]
[49]
[37]
[26]
[62]
[38]
[55]
[24]
[30]
[39]
[59]
[26]
[33]
[20]
[18]
[19]
[61]
[39]
[52]
[20]
[50]
[29]
[55]
[18]
[39]
[35]
[38]
[20]
[60]
[61]
[62]
[21]
[40]
[25]
[50]
[24]
[28]
[22]
[22]
[27]
[54]
[25]
[25]
[30]
[59]
[51]
[38]
[28]
[30]
[43]
[42]
[24]
[47]
[23]
[59]
[22]
[27]
[65]
[27]
[27]
[28]
[22]
[42]
[25]
[41]
[46]
[41]
[29]
[50]
[50]
[34]
[24]
[29]
[35]
[24]
[23]
[31]
[24]
[30]
[22]
[43]
[55]
[38]
[28]
[30]
[35]
[41]
[28]
[65]
[20]
[39]
[19]
[64]
[42]
[24]
[24]
[18]
[36]
[61]
[22]
[55]
[27]
[49]
[29]
[33]
[52]
[26]

{"sheet":"EstMeanGroupedData (an)","index":43,"n_rows":201,"n_cols":16,"rows_kept":201,"cut":false,"hidden":false,"merged":[]}
["Age",null,null,null,"Quantitative: Integer, COUNTIFS",null,null,null,null,null,null,null,null,null,null,19]
[21,null,"Lower","Upper","Age","Frequency",null,"Midpoint",null,null,null,null,null,"Min"]
[57,null,0,{"$f":"C3+$P$1","v":19},{"$f":"C3&\" - \"&D3","v":"0 - 19"},{"$f":"COUNTIFS($A$2:$A$201,\">=\"&C3,$A$2:$A$201,\"<=\"&D3)","v":13},null,{"$f":"AVERAGE(C3:D3)","v":9.5},null,null,null,null,null,{"$f":"MIN($A$2:$A$201)","v":18}]
[25,null,{"$f":"D3+1","v":20},{"$f":"C4+$P$1","v":39},{"$f":"C4&\" - \"&D4","v":"20 - 39"},{"$f":"COUNTIFS($A$2:$A$201,\">=\"&C4,$A$2:$A$201,\"<=\"&D4)","v":110},null,{"$f":"AVERAGE(C4:D4)","v":29.5},null,null,null,null,null,"Max"]
[38,null,{"$f":"D4+1","v":40},{"$f":"C5+$P$1","v":59},{"$f":"C5&\" - \"&D5","v":"40 - 59"},{"$f":"COUNTIFS($A$2:$A$201,\">=\"&C5,$A$2:$A$201,\"<=\"&D5)","v":56},null,{"$f":"AVERAGE(C5:D5)","v":49.5},null,null,null,null,null,{"$f":"MAX($A$2:$A$201)","v":65}]
[22,null,{"$f":"D5+1","v":60},{"$f":"C6+$P$1","v":79},{"$f":"C6&\" - \"&D6","v":"60 - 79"},{"$f":"COUNTIFS($A$2:$A$201,\">=\"&C6,$A$2:$A$201,\"<=\"&D6)","v":21},null,{"$f":"AVERAGE(C6:D6)","v":69.5}]
[29,null,null,null,"Total",{"$f":"SUM(F3:F6)","v":200}]
[18]
[64,null,null,null,"Average Age",{"$f":"AVERAGE(A2:A201)","v":37.08}]
[27]
[22,null,null,null,"Average Age from Grouped Data",{"$f":"SUMPRODUCT(F3:F6,H3:H6)/F7","v":38}]
[39,null,null,null,"** will not be the same as actual mean because we are"]
[61,null,null,null,"estimating the data points when we use midpoint for the"]
[18,null,null,null,"unknown data points"]
[22]
[52]
[22]
[18]
[55]
[20]
[42]
[30]
[64]
[63]
[41]
[21]
[63]
[54]
[18]
[26]
[59]
[30]
[64]
[30]
[41]
[23]
[52]
[18]
[32]
[22]
[29]
[25]
[63]
[26]
[31]
[23]
[42]
[28]
[23]
[19]
[37]
[38]
[50]
[26]
[33]
[59]
[32]
[27]
[54]
[63]
[48]
[29]
[38]
[24]
[51]
[25]
[65]
[35]
[35]
[21]
[47]
[62]
[63]
[23]
[59]
[48]
[57]
[19]
[48]
[21]
[40]
[25]
[59]
[57]
[56]
[19]
[54]
[65]
[25]
[30]
[57]
[43]
[44]
[21]
[20]
[49]
[37]
[26]
[62]
[38]
[55]
[24]
[30]
[39]
[59]
[26]
[33]
[20]
[18]
[19]
[61]
[39]
[52]
[20]
[50]
[29]
[55]
[18]
[39]
[35]
[38]
[20]
[60]
[61]
[62]
[21]
[40]
[25]
[50]
[24]
[28]
[22]
[22]
[27]
[54]
[25]
[25]
[30]
[59]
[51]
[38]
[28]
[30]
[43]
[42]
[24]
[47]
[23]
[59]
[22]
[27]
[65]
[27]
[27]
[28]
[22]
[42]
[25]
[41]
[46]
[41]
[29]
[50]
[50]
[34]
[24]
[29]
[35]
[24]
[23]
[31]
[24]
[30]
[22]
[43]
[55]
[38]
[28]
[30]
[35]
[41]
[28]
[65]
[20]
[39]
[19]
[64]
[42]
[24]
[24]
[18]
[36]
[61]
[22]
[55]
[27]
[49]
[29]
[33]
[52]
[26]

{"sheet":"Geomean","index":44,"n_rows":14,"n_cols":7,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["Percentage increase for stock value each year",null,null,"Geometric mean 1: Use if you are averaging percentage change over time for the % change + 1 = "]
["% change",{"$f":"A2&\" + 1\"","v":"% change + 1"},null,"Count"]
[0.15,null,null,"Formula",null,"(GM1 = X1*X2*…Xn)^(1/n)-1"]
[0.12,null,null,"GEOMEAN",null,"GEOMEAN function"]
[0.13,null,null,"Mean > GM"]
[0.16]
[0.21,null,null,"Geometric mean 2: Use if you have begin number and end number and you know the number of periods"]
[0.185,null,null,null,"Year","Stock Price (Split Adj)"]
[0.19,null,null,{"$f":"\"Whole Foods Stock Price \"&E9","v":"Whole Foods Stock Price 1992"},1992,6.75]
[0.02,null,null,{"$f":"\"Whole Foods Stock Price \"&E10","v":"Whole Foods Stock Price 2005"},2005,153.94]
[0.05]
[null,null,null,null,"Periods = n"]
[null,null,null,null,"GEOMEAN",null,"(End/Beg)^(1/n)-1"]
[null,null,null,null,"check:"]

{"sheet":"GeomeanAN","index":45,"n_rows":14,"n_cols":7,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["Percentage increase for stock value each year",null,null,"Geometric mean 1: Use if you are averaging percentage change over time for the % change + 1 = "]
["% change",{"$f":"A2&\" + 1\"","v":"% change + 1"},null,"Count",{"$f":"COUNT(B3:B11)","v":9}]
[0.15,{"$f":"1+A3","v":1.1499999999999999},null,"Formula",{"$f":"PRODUCT(B3:B11)^(1/E2)-1","v":0.13335464167659472},"(GM1 = X1*X2*…Xn)^(1/n)-1"]
[0.12,{"$f":"1+A4","v":1.1200000000000001},null,"GEOMEAN",{"$f":"GEOMEAN(B3:B11)-1","v":0.13335464167659472},"GEOMEAN function"]
[0.13,1.1299999999999999,null,"Mean > GM",{"$f":"AVERAGE(A3:A11)","v":0.13500000000000001}]
[0.16,1.1599999999999999]
[0.21,1.21,null,"Geometric mean 2: Use if you have begin number and end number and you know the number of periods"]
[0.185,1.1850000000000001,null,null,"Year","Stock Price (Split Adj)"]
[0.19,1.19,null,{"$f":"\"Whole Foods Stock Price \"&E9","v":"Whole Foods Stock Price 1992"},1992,6.75]
[0.02,1.02,null,{"$f":"\"Whole Foods Stock Price \"&E10","v":"Whole Foods Stock Price 2005"},2005,153.94]
[0.05,1.05]
[null,null,null,null,"Periods = n",{"$f":"E10-E9","v":13}]
[null,null,null,null,"GEOMEAN",{"$f":"(F10/F9)^(1/F12)-1","v":0.27193585047850655},"(End/Beg)^(1/n)-1"]
[null,null,null,null,"check:",{"$f":"F9*(1+F13)^F12","v":153.93999999999994}]

{"sheet":"Trimmed Mean","index":46,"n_rows":40,"n_cols":5,"rows_kept":40,"cut":false,"hidden":false,"merged":[]}
["Remove 5% of smallest and largest values from data set. Then calculate the Mean"]
[null,null,null,"trim",0.05]
["No","Salaries",null,"n ="]
[1,1020,null,"# values to drop"]
[2,1030,null,"Round up to integer"]
[3,2150,null,"Method 1"]
[4,2861,null,"Trimmed Mean"]
[5,2864]
[6,2964]
[7,2983]
[8,3087,null,"Method 2 (Dynamic)"]
[9,3167,null,"Trimmed Mean",{"$f":"IF(E5=\"\",\"\",AVERAGE(OFFSET(B4,E5,,E3-E5*2)))","v":""}]
[10,3222]
[11,3234]
[12,3267]
[13,3275]
[14,3283]
[15,3334]
[16,3336]
[17,3337]
[18,3440]
[19,3442]
[20,3480]
[21,3485]
[22,3509]
[23,3546]
[24,3609]
[25,3626]
[26,3628]
[27,3633]
[28,3658]
[29,3796]
[30,3814]
[31,3875]
[32,3901]
[33,3946]
[34,5900]
[35,6200]
[36,7200]
[37,8440]

{"sheet":"Trimmed MeanAN","index":47,"n_rows":40,"n_cols":5,"rows_kept":40,"cut":false,"hidden":false,"merged":[]}
["Remove 5% of smallest and largest values from data set. Then calculate the Mean"]
[null,null,null,"trim",0.05]
["No","Salaries",null,"n =",{"$f":"COUNT(B4:B40)","v":37}]
[1,1020,null,"# values to drop",{"$f":"E3*E2","v":1.85}]
[2,1030,null,"Round up to integer",{"$f":"ROUNDUP(E4,0)","v":2}]
[3,2150,null,"Method 1"]
[4,2861,null,"Trimmed Mean",{"$f":"AVERAGE(B6:B38)","v":3540.969696969697}]
[5,2864]
[6,2964]
[7,2983]
[8,3087,null,"Method 2 (Dynamic)"]
[9,3167,null,"Trimmed Mean",{"$f":"AVERAGE(OFFSET(B4,E5,,E3-E5*2))","v":3540.969696969697}]
[10,3222]
[11,3234]
[12,3267]
[13,3275]
[14,3283]
[15,3334]
[16,3336]
[17,3337]
[18,3440]
[19,3442]
[20,3480]
[21,3485]
[22,3509]
[23,3546]
[24,3609]
[25,3626]
[26,3628]
[27,3633]
[28,3658]
[29,3796]
[30,3814]
[31,3875]
[32,3901]
[33,3946]
[34,5900]
[35,6200]
[36,7200]
[37,8440]

{"sheet":"V(1)","index":48,"n_rows":19,"n_cols":3,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["Based on Average Returns, which stock do you prefer?"]
[]
["Year","Stock Return A","Stock Return B"]
[1995,0.05,0.02]
[1996,0.1,0.04]
[1997,0.12,3.5000000000000003E-2]
[1998,0.17,5.5E-2]
[1999,0.19,0.04]
[2000,0.01,4.2000000000000003E-2]
[2001,-0.15,4.2999999999999997E-2]
[2002,-0.03,4.7E-2]
[2003,0.03,0.05]
[2004,5.5E-2,5.0999999999999997E-2]
[2005,0.1,0.03]
[2006,6.5000000000000002E-2,2.9000000000000001E-2]
[2007,-0.02,4.5999999999999999E-2]
[2008,-0.22,4.9000000000000002E-2]
[2009,0.15,4.1000000000000002E-2]
["Mean"]

{"sheet":"V(1an)","index":49,"n_rows":19,"n_cols":3,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["Based on Average Returns, which stock do you prefer?"]
[]
["Year","Stock Return A","Stock Return B"]
[1995,0.05,0.02]
[1996,0.1,0.04]
[1997,0.12,3.5000000000000003E-2]
[1998,0.17,5.5E-2]
[1999,0.19,0.04]
[2000,0.01,4.2000000000000003E-2]
[2001,-0.15,4.2999999999999997E-2]
[2002,-0.03,4.7E-2]
[2003,0.03,0.05]
[2004,5.5E-2,5.0999999999999997E-2]
[2005,0.1,0.03]
[2006,6.5000000000000002E-2,2.9000000000000001E-2]
[2007,-0.02,4.5999999999999999E-2]
[2008,-0.22,4.9000000000000002E-2]
[2009,0.15,4.1000000000000002E-2]
["Mean",{"$f":"AVERAGE(B4:B18)","v":4.1333333333333347E-2},{"$f":"AVERAGE(C4:C18)","v":4.1200000000000007E-2}]

{"sheet":"V(2)","index":50,"n_rows":25,"n_cols":3,"rows_kept":25,"cut":false,"hidden":false,"merged":[]}
["Based on Average Returns, which stock do you prefer?\nIt is hard to know, without looking at the volatility of past stock returns."]
["Variability"]
["Dispersion"]
["Spread In Data"]
["How Spread Out Is Data?"]
["Are the Data Points Clustered Around the Mean?"]
["Does the Mean Fairly Represent the Data Points?"]
[]
["Mean",{"$f":"AVERAGE(B11:B25)","v":4.1333333333333347E-2},{"$f":"AVERAGE(C11:C25)","v":4.1200000000000007E-2}]
["Year","Stock Return A","Stock Return B"]
[1995,0.05,0.02]
[1996,0.1,0.04]
[1997,0.12,3.5000000000000003E-2]
[1998,0.17,5.5E-2]
[1999,0.19,0.04]
[2000,0.01,4.2000000000000003E-2]
[2001,-0.15,4.2999999999999997E-2]
[2002,-0.03,4.7E-2]
[2003,0.03,0.05]
[2004,5.5E-2,5.0999999999999997E-2]
[2005,0.1,0.03]
[2006,6.5000000000000002E-2,2.9000000000000001E-2]
[2007,-0.02,4.5999999999999999E-2]
[2008,-0.22,4.9000000000000002E-2]
[2009,0.15,4.1000000000000002E-2]

{"sheet":"V(3)","index":51,"n_rows":29,"n_cols":7,"rows_kept":29,"cut":false,"hidden":false,"merged":[]}
["Variability"]
["Dispersion"]
["Spread In Data"]
["How Spread Out Is Data?"]
["Are the Data Points Clustered Around the Mean?"]
["Does the Mean Fairly Represent the Data Points?"]
["Visually Portray Variability"]
["Create X-Y Scatter Diagram"]
["Go to Design Ribbon, Data Group, Select Data to Add Data Series"]
[]
[null,null,"X","Mean Stock A",null,"X","Mean Stock B"]
["Mean",null,{"$f":"AVERAGE(C15:C29)","v":4.1333333333333347E-2},null,null,{"$f":"AVERAGE(F15:F29)","v":4.1200000000000007E-2}]
[]
["Year",null,"Stock Return A, X","Stock Returns A",null,"Stock Return B, X","Stock Returns B"]
[1995,null,0.05,null,null,0.02]
[1996,null,0.1,null,null,0.04]
[1997,null,0.12,null,null,3.5000000000000003E-2]
[1998,null,0.17,null,null,5.5E-2]
[1999,null,0.19,null,null,0.04]
[2000,null,0.01,null,null,4.2000000000000003E-2]
[2001,null,-0.15,null,null,4.2999999999999997E-2]
[2002,null,-0.03,null,null,4.7E-2]
[2003,null,0.03,null,null,0.05]
[2004,null,5.5E-2,null,null,5.0999999999999997E-2]
[2005,null,0.1,null,null,0.03]
[2006,null,6.5000000000000002E-2,null,null,2.9000000000000001E-2]
[2007,null,-0.02,null,null,4.5999999999999999E-2]
[2008,null,-0.22,null,null,4.9000000000000002E-2]
[2009,null,0.15,null,null,4.1000000000000002E-2]

{"sheet":"V(3an)","index":52,"n_rows":29,"n_cols":7,"rows_kept":29,"cut":false,"hidden":false,"merged":[]}
["Variability"]
["Dispersion"]
["Spread In Data"]
["How Spread Out Is Data?"]
["Are the Data Points Clustered Around the Mean?"]
["Does the Mean Fairly Represent the Data Points?"]
["Visually Portray Variability"]
["Create X-Y Scatter Diagram"]
["Go to Design Ribbon, Data Group, Select Data to Add Data Series"]
[]
[null,null,"X","Stock A Mean",null,"X","Stock B Mean"]
["Mean",null,{"$f":"AVERAGE(C15:C29)","v":4.1333333333333347E-2},1,null,{"$f":"AVERAGE(F15:F29)","v":4.1200000000000007E-2},3]
[]
["Year",null,"Stock Return A, X","Stock Return A",null,"Stock Return B, X","Stock Return B"]
[1995,null,0.05,2,null,0.02,4]
[1996,null,0.1,2,null,0.04,4]
[1997,null,0.12,2,null,3.5000000000000003E-2,4]
[1998,null,0.17,2,null,5.5E-2,4]
[1999,null,0.19,2,null,0.04,4]
[2000,null,0.01,2,null,4.2000000000000003E-2,4]
[2001,null,-0.15,2,null,4.2999999999999997E-2,4]
[2002,null,-0.03,2,null,4.7E-2,4]
[2003,null,0.03,2,null,0.05,4]
[2004,null,5.5E-2,2,null,5.0999999999999997E-2,4]
[2005,null,0.1,2,null,0.03,4]
[2006,null,6.5000000000000002E-2,2,null,2.9000000000000001E-2,4]
[2007,null,-0.02,2,null,4.5999999999999999E-2,4]
[2008,null,-0.22,2,null,4.9000000000000002E-2,4]
[2009,null,0.15,2,null,4.1000000000000002E-2,4]

{"sheet":"V(4)","index":53,"n_rows":24,"n_cols":8,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
["Variability"]
["Dispersion"]
["Spread In Data"]
["How Spread Out Is Data?"]
["Are the Data Points Clustered Around the Mean?"]
["Does the Mean Fairly Represent the Data Points?"]
[]
["Mean",{"$f":"AVERAGE(B10:B24)","v":4.1333333333333347E-2},{"$f":"AVERAGE(C10:C24)","v":4.1200000000000007E-2},null,"Range"]
["Year","Stock Return A","Stock Return B",null,"Max - Min"]
[1995,0.05,0.02,null,"Simple to calculate. It is very sensitive to the smallest and largest data values (extreme values)."]
[1996,0.1,0.04]
[1997,0.12,3.5000000000000003E-2,null,null,"Stock Return A","Stock Return B"]
[1998,0.17,5.5E-2,null,"Max"]
[1999,0.19,0.04,null,"Min"]
[2000,0.01,4.2000000000000003E-2,null,"Range"]
[2001,-0.15,4.2999999999999997E-2]
[2002,-0.03,4.7E-2,null,"Interquartile Range"]
[2003,0.03,0.05,null,"Quartile 3 - Quartile 1"]
[2004,5.5E-2,5.0999999999999997E-2,null,"The range for the middle 50% of the data. It overcomes the sensitivity to extreme data values."]
[2005,0.1,0.03]
[2006,6.5000000000000002E-2,2.9000000000000001E-2,null,{"$f":"\"Quartile \"&H21","v":"Quartile 1"},null,null,1]
[2007,-0.02,4.5999999999999999E-2,null,{"$f":"\"Quartile \"&H22","v":"Quartile 3"},null,null,3]
[2008,-0.22,4.9000000000000002E-2,null,"Interquartile Range"]
[2009,0.15,4.1000000000000002E-2]

{"sheet":"V(4an)","index":54,"n_rows":24,"n_cols":8,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
["Variability"]
["Dispersion"]
["Spread In Data"]
["How Spread Out Is Data?"]
["Are the Data Points Clustered Around the Mean?"]
["Does the Mean Fairly Represent the Data Points?"]
[]
["Mean",{"$f":"AVERAGE(B10:B24)","v":4.1333333333333347E-2},{"$f":"AVERAGE(C10:C24)","v":4.1200000000000007E-2},null,"Range"]
["Year","Stock Return A","Stock Return B",null,"Max - Min"]
[1995,0.05,0.02,null,"Simple to calculate. It is very sensitive to the smallest and largest data values (extreme values)."]
[1996,0.1,0.04]
[1997,0.12,3.5000000000000003E-2,null,null,"Stock Return A","Stock Return B"]
[1998,0.17,5.5E-2,null,"Max",{"$f":"MAX(B10:B24)","v":0.19},{"$f":"MAX(C10:C24)","v":5.5E-2}]
[1999,0.19,0.04,null,"Min",{"$f":"MIN(B10:B24)","v":-0.22},{"$f":"MIN(C10:C24)","v":0.02}]
[2000,0.01,4.2000000000000003E-2,null,"Range",{"$f":"F13-F14","v":0.41000000000000003},{"$f":"G13-G14","v":3.5000000000000003E-2}]
[2001,-0.15,4.2999999999999997E-2]
[2002,-0.03,4.7E-2,null,"Interquartile Range"]
[2003,0.03,0.05,null,"Quartile 3 - Quartile 1"]
[2004,5.5E-2,5.0999999999999997E-2,null,"The range for the middle 50% of the data. It overcomes the sensitivity to extreme data values."]
[2005,0.1,0.03]
[2006,6.5000000000000002E-2,2.9000000000000001E-2,null,{"$f":"\"Quartile \"&H21","v":"Quartile 1"},{"$f":"_xlfn.QUARTILE.INC(B$10:B$24,$H21)","v":-5.000000000000001E-3},{"$f":"_xlfn.QUARTILE.INC(C$10:C$24,$H21)","v":3.7500000000000006E-2},1]
[2007,-0.02,4.5999999999999999E-2,null,{"$f":"\"Quartile \"&H22","v":"Quartile 3"},{"$f":"_xlfn.QUARTILE.INC(B$10:B$24,$H22)","v":0.11},{"$f":"_xlfn.QUARTILE.INC(C$10:C$24,$H22)","v":4.8000000000000001E-2},3]
[2008,-0.22,4.9000000000000002E-2,null,"Interquartile Range",{"$f":"F22-F21","v":0.115},{"$f":"G22-G21","v":1.0499999999999995E-2}]
[2009,0.15,4.1000000000000002E-2]

{"sheet":"V(5)","index":55,"n_rows":36,"n_cols":8,"rows_kept":36,"cut":false,"hidden":false,"merged":[]}
["Deviation"]
["How far one datum is from the mean"]
["Sample Standard Deviation"]
["A Numerical Measure that says how much variability there is in the data points."]
["Standard Deviation Is Like An Average Of The Deviations"]
["Standard Deviation tells us how fairly the mean represents its data points"]
["Standard Deviation tells us how clustered the data points are around the mean."]
[]
["Based on Average Returns, which stock do you prefer?\nIt is hard to know, without looking at the volitility of past stock returns."]
["Count"]
["Count -1",null,null,null,null,"Sample data divided by just the count underestimates"]
["Mean = Xbar",null,null,null,null,"What minus one does: 10/5 = 2, but 10/(5-1) = 2.5"]
["Year","Stock Return A","Deviation","Deviation ^2","Stock Return B","Deviation","Deviation ^2"]
[1995,0.05,null,null,0.02]
[1996,0.1,null,null,0.04]
[1997,0.12,null,null,3.5000000000000003E-2]
[1998,0.17,null,null,5.5E-2]
[1999,0.19,null,null,0.04]
[2000,0.01,null,null,4.2000000000000003E-2]
[2001,-0.15,null,null,4.2999999999999997E-2]
[2002,-0.03,null,null,4.7E-2]
[2003,0.03,null,null,0.05]
[2004,5.5E-2,null,null,5.0999999999999997E-2]
[2005,0.1,null,null,0.03]
[2006,6.5000000000000002E-2,null,null,2.9000000000000001E-2]
[2007,-0.02,null,null,4.5999999999999999E-2]
[2008,-0.22,null,null,4.9000000000000002E-2]
[2009,0.15,null,null,4.1000000000000002E-2]
[null,"Total"]
[]
[null,"Sample Variance = s2",null,null,null,null,null,"Units are squared"]
[null,"Sample Standard Deviation = s",null,null,null,null,null,"Square root to get back to same unit"]
[null,null,null,null,null,null,null,"STDEV.S (Standard Deviation for Sample)"]
[null,null,null,null,null,null,null,"The sample SD, s, is a point estimator  of the population SD, sigma σ"]
[null,null,null,null,null,null,null,"s = Numerical Measure of Risk of Stock (Volitility)"]
[null,null,null,null,null,null,null,"Which mean more fairly represnets its data points?"]

{"sheet":"VariabilityNotesxx","index":56,"n_rows":44,"n_cols":11,"rows_kept":44,"cut":false,"hidden":true,"merged":[]}
["Measures of Variability (Dispersion)"]
["How Spread Out Is The Data?"]
["Does the mean fairly represent the data? Are the data clustered around the mean, or not?"]
[]
["Range","Max - Min"]
[null,"Simple to calculate. It is very sensitive to the smallest and largest data values (extreme values)."]
["Interquartile Range","Quartile 3 - Quartile 1"]
[null,"The range for the middle 50% of the data. It overcomes the sensitivity to extreme data values."]
["Deviation","How far one datum is from the mean"]
["Population Variance ","Sum of square of each deviation divided by number of values"]
["Sample Variance ","Sum of square of each deviation divided by number of values minus 1"]
[null,"The variance is a measure of variability that utilizes all the data."]
[null,"But the units are squared"]
["Population Standard Deviation","Square root of population variance "]
["Sample Standard Deviation","Square root of sample variance "]
[null,"The standard deviation is a measure of variability that utilizes all the data."]
[null,"But the units are not squared"]
[]
["Sample","Sample"]
["Colorado Boomerangs - Boomerangs Made per day","Gel Boomerangs - Boomerangs Made per day",null,null,"Colorado","Gel"]
["X","X",null,"Mean",{"$f":"AVERAGE(A22:A31)","v":60},{"$f":"AVERAGE(B22:B31)","v":60},"The sample mean, Xbar, is a point estimator of the population mean μ"]
[60,60,null,"Max",{"$f":"MAX(A22:A31)","v":64},{"$f":"MAX(B22:B31)","v":80}]
[60,60,null,"Min",{"$f":"MIN(A22:A31)","v":56},{"$f":"MIN(B22:B31)","v":40}]
[60,60,null,"Range",{"$f":"E22-E23","v":8},{"$f":"F22-F23","v":40}]
[60,60]
[58,72,null,"Colo X","Deviations (X - Xbar)","(X-Xbar)^2",null,"Gel X","Deviations (X - Xbar)","(X-Xbar)^2"]
[58,72,null,{"$f":"A22","v":60},{"$f":"D27-$E$21","v":0},{"$f":"E27^2","v":0},null,{"$f":"B22","v":60},{"$f":"H27-$F$21","v":0},{"$f":"I27^2","v":0}]
[56,80,null,{"$f":"A23","v":60},0,0,null,60,0,0]
[62,48,null,60,0,0,null,60,0,0]
[62,48,null,60,0,0,null,60,0,0]
[64,40,null,58,-2,4,null,72,12,144]
[null,null,null,58,-2,4,null,72,12,144]
[null,null,null,56,-4,16,null,80,20,400]
[null,null,null,62,2,4,null,48,-12,144]
[null,null,null,62,2,4,null,48,-12,144]
[null,null,null,64,4,16,null,40,-20,400]
[null,null,null,"Add All Deviations",{"$f":"SUM(E27:E36)","v":0},{"$f":"SUM(F27:F36)","v":48},null,"Add All Deviations",{"$f":"SUM(I27:I36)","v":0},{"$f":"SUM(J27:J36)","v":1376}]
[null,null,null,null,"Count - 1",{"$f":"COUNT(D27:D36)-1","v":9},null,null,"Count - 1",{"$f":"COUNT(H27:H36)-1","v":9}]
[null,null,null,"s^2","Variance",{"$f":"F37/F38","v":5.333333333333333},"but units are squared",null,"Variance",{"$f":"J37/J38","v":152.88888888888889},"but units are squared"]
[null,null,null,"s^2","VAR function for Sample Variance",{"$f":"VAR(D27:D36)","v":5.333333333333333},null,null,"VAR function for Sample Variance",{"$f":"VAR(H27:H36)","v":152.88888888888889}]
[null,null,null,"s","Standard Deviation",{"$f":"F40^(1/2)","v":2.3094010767585029},"raised to 1/2",null,"Standard Deviation",{"$f":"J40^(1/2)","v":12.364824660660938},"raised to 1/2"]
[null,null,null,"s","Standard Deviation",{"$f":"SQRT(F40)","v":2.3094010767585029},"SQRT function",null,"Standard Deviation",{"$f":"SQRT(J40)","v":12.364824660660938},"SQRT function"]
[null,null,null,"s","STDEV function for Sample Standard Deviation",{"$f":"STDEV(D27:D36)","v":2.3094010767585029},null,null,"STDEV function for Sample Standard Deviation",{"$f":"STDEV(H27:H36)","v":12.364824660660938}]
[null,null,null,null,null,"The sample SD, s, is a point estimator  of the population SD, sigma σ"]

{"sheet":"V(3xxxx)","index":57,"n_rows":19,"n_cols":8,"rows_kept":19,"cut":false,"hidden":true,"merged":[]}
["Variability"]
["Spread In Data"]
["How Spread Out Is Data?"]
["Are the Data Points Clustered Around the Mean?"]
["Does the Mean Fairly Represent the Data Points?"]
["Wage Data",null,"Wage Data"]
["X - 1","Y - 1","X - 2","Y - 2",null,"Mean 1",{"$f":"AVERAGE(A8:A12)","v":14},1]
[12,2,8,4,null,"Mean 2",{"$f":"AVERAGE(C8:C12)","v":14.000000000000009},3]
[15,2,15,4]
[19,2,22,4]
[13,2,7,4]
[11,2,18.000000000000039,4]
[]
[]
[]
[]
["Visually Portray Variability"]
["Create X-Y Scatter Diagram"]
["Go to Design Ribbon, Data Group, Select Data to Add Data Series"]

{"sheet":"V(4xxxx)","index":58,"n_rows":11,"n_cols":6,"rows_kept":11,"cut":false,"hidden":true,"merged":[]}
["Range"]
["Max - Min"]
["Simple to calculate. It is very sensitive to the smallest and largest data values (extreme values)."]
["Wage Data"]
[]
["Sample1","Sample2",null,null,{"$f":"A6","v":"Sample1"},{"$f":"B6","v":"Sample2"}]
[12,8,null,"MIN",{"$f":"MIN(A7:A11)","v":11},{"$f":"MIN(B7:B11)","v":7}]
[15,15,null,"MAX",{"$f":"MAX(A7:A11)","v":19},{"$f":"MAX(B7:B11)","v":22}]
[19,22,null,"Range",{"$f":"E8-E7","v":8},{"$f":"F8-F7","v":15}]
[13,7]
[11,18.000000000000039]

{"sheet":"V(5xxxx)","index":59,"n_rows":130,"n_cols":7,"rows_kept":130,"cut":false,"hidden":true,"merged":[]}
["Interquartile Range"]
["Quartile 3 - Quartile 1"]
["The range for the middle 50% of the data. It overcomes the sensitivity to extreme data values."]
["Wage Data"]
[]
["Sample1","Sample2",null,null,{"$f":"A6","v":"Sample1"},{"$f":"B6","v":"Sample2"}]
[12,8,null,"Quartile 1",{"$f":"QUARTILE(A$7:A$130,$G7)","v":12},{"$f":"QUARTILE(B$7:B$130,$G7)","v":10},1]
[15,15,null,"Quartile 3",{"$f":"QUARTILE(A$7:A$130,$G8)","v":17.25},{"$f":"QUARTILE(B$7:B$130,$G8)","v":18},3]
[19,22,null,"Interquartile Range",{"$f":"E8-E7","v":5.25},{"$f":"F8-F7","v":8}]
[13,7]
[11,18.000000000000039,null,null,{"$f":"E6","v":"Sample1"},{"$f":"F6","v":"Sample2"}]
[11,10,null,"MIN",{"$f":"MIN(A7:A130)","v":10},{"$f":"MIN(B7:B130)","v":6}]
[12,9,null,"MAX",{"$f":"MAX(A7:A130)","v":19},{"$f":"MAX(B7:B130)","v":22}]
[16,16,null,"Range",{"$f":"E13-E12","v":9},{"$f":"F13-F12","v":16}]
[14,18]
[15,17]
[11,18]
[13,13]
[18,20]
[17,11]
[18,11]
[16,20]
[11,13]
[13,15]
[19,17]
[18,18]
[19,9]
[18,11]
[15,8]
[19,18]
[14,11]
[10,16]
[16,20]
[14,17]
[19,18]
[12,9]
[18,16]
[17,20]
[16,16]
[16,16]
[14,19]
[12,20]
[16,18]
[14,17]
[18,10]
[10,12]
[18,16]
[17,7]
[13,20]
[13,20]
[12,16]
[12,20]
[11,18]
[12,6]
[18,9]
[19,13]
[12,12]
[18,9]
[17,19]
[13,6]
[13,6]
[13,19]
[11,10]
[14,19]
[10,11]
[14,20]
[16,14]
[14,8]
[12,16]
[10,11]
[13,16]
[13,13]
[18,14]
[12,18]
[18,12]
[11,12]
[18,14]
[10,20]
[18,18]
[14,6]
[13,12]
[19,8]
[18,14]
[14,8]
[13,15]
[17,11]
[14,14]
[12,10]
[16,7]
[16,16]
[10,20]
[17,10]
[18,12]
[11,6]
[17,11]
[16,16]
[17,11]
[18,8]
[12,9]
[13,16]
[10,15]
[18,11]
[17,15]
[17,9]
[15,12]
[14,18]
[14,6]
[12,13]
[14,13]
[13,13]
[12,6]
[13,20]
[16,6]
[10,14]
[17,19]
[14,16]
[19,20]
[19,8]
[14,17]
[11,8]
[18,10]
[19,18]
[11,7]
[15,20]
[14,13]
[18,11]
[19,19]
[17,18]
[11,6]
[19,13]

{"sheet":"V(6xxxx)","index":60,"n_rows":35,"n_cols":7,"rows_kept":35,"cut":false,"hidden":true,"merged":[]}
["Deviation"]
["How far one datum is from the mean"]
["Sample Standard Deviation"]
["A Numerical Measure that says how much variability there is in the data points."]
["Standard Deviation Is Like An Average Of The Deviations"]
["Standard Deviation tells us how fairly the mean represents its data points"]
["Standard Deviation tells us how clustered the data points are around the mean."]
[]
["Wage Data",null,null,"Mean1","Count","Count - 1","Sample data divided by just the count underestimates"]
[null,null,null,{"$f":"AVERAGE(A12:A16)","v":14},{"$f":"COUNT(A12:A16)","v":5},{"$f":"E10-1","v":4},"What minus one does: 10/5 = 2, but 10/(5-1) = 2.5"]
["Sample1","Sample2",null,"X","X - Xbar","(X - Xbar)^2"]
[12,8,null,{"$f":"A12","v":12},{"$f":"D12-$D$10","v":-2},{"$f":"E12^2","v":4}]
[15,15,null,{"$f":"A13","v":15},{"$f":"D13-$D$10","v":1},{"$f":"E13^2","v":1}]
[19,22,null,{"$f":"A14","v":19},{"$f":"D14-$D$10","v":5},{"$f":"E14^2","v":25}]
[13,7,null,{"$f":"A15","v":13},{"$f":"D15-$D$10","v":-1},{"$f":"E15^2","v":1}]
[11,18.000000000000039,null,{"$f":"A16","v":11},{"$f":"D16-$D$10","v":-3},{"$f":"E16^2","v":9}]
[null,null,null,"Total",{"$f":"SUM(E12:E16)","v":0},{"$f":"SUM(F12:F16)","v":40}]
[null,null,null,null,"Variance",{"$f":"F17/F10","v":10},"Units are squared"]
[null,null,null,null,"Standard Deviation",{"$f":"F18^(1/2)","v":3.1622776601683795},"Units are not squared"]
[null,null,null,null,"Standard Deviation",{"$f":"SQRT(F18)","v":3.1622776601683795}]
[null,null,null,null,"The sample SD, s, is a point estimator  of the population SD, sigma σ"]
[null,null,null,"Mean2","Count","Count - 1","Sample data divided by just the count underestimates"]
[null,null,null,{"$f":"AVERAGE(B12:B16)","v":14.000000000000009},{"$f":"COUNT(B12:B16)","v":5},{"$f":"E23-1","v":4},"What minus one does: 10/5 = 2, but 10/(5-1) = 2.5"]
[null,null,null,"X","X - Xbar"]
[null,null,null,{"$f":"B12","v":8},{"$f":"D25-$D$23","v":-6.0000000000000089},{"$f":"E25^2","v":36.000000000000107}]
[null,null,null,{"$f":"B13","v":15},{"$f":"D26-$D$23","v":0.99999999999999112},{"$f":"E26^2","v":0.99999999999998224}]
[null,null,null,{"$f":"B14","v":22},{"$f":"D27-$D$23","v":7.9999999999999911},{"$f":"E27^2","v":63.999999999999858}]
[null,null,null,{"$f":"B15","v":7},{"$f":"D28-$D$23","v":-7.0000000000000089},{"$f":"E28^2","v":49.000000000000128}]
[null,null,null,{"$f":"B16","v":18.000000000000039},{"$f":"D29-$D$23","v":4.0000000000000302},{"$f":"E29^2","v":16.000000000000242}]
[null,null,null,"Total",null,{"$f":"SUM(F25:F29)","v":166.00000000000028}]
[null,null,null,null,{"$f":"E18","v":"Variance"},{"$f":"F30/F23","v":41.500000000000071},"Units are squared"]
[null,null,null,null,"Standard Deviation",{"$f":"SQRT(F31)","v":6.4420493633625684},"Units are not squared"]
[null,null,null,null,"The sample SD, s, is a point estimator  of the population SD, sigma σ"]
[null,null,null,"Conclusion:"]
[null,null,null,"Although the two have the same means, the variability, as measured by standard deviation, is much larger for the Sample 2 data. The mean for the sample 1 data represents it data points more fairly than the mean for the sample 2 data represents it data points."]

{"sheet":"V(5an)","index":61,"n_rows":36,"n_cols":8,"rows_kept":36,"cut":false,"hidden":false,"merged":[]}
["Deviation"]
["How far one datum is from the mean"]
["Sample Standard Deviation"]
["A Numerical Measure that says how much variability there is in the data points."]
["Standard Deviation Is Like An Average Of The Deviations"]
["Standard Deviation tells us how fairly the mean represents its data points"]
["Standard Deviation tells us how clustered the data points are around the mean."]
[]
["Based on Average Returns, which stock do you prefer?\nIt is hard to know, without looking at the volitility of past stock returns."]
["Count",{"$f":"COUNT(B14:B28)","v":15},null,null,{"$f":"COUNT(E14:E28)","v":15}]
["Count -1",{"$f":"B10-1","v":14},null,null,{"$f":"E10-1","v":14},"Sample data divided by just the count underestimates"]
["Mean = Xbar",{"$f":"AVERAGE(B14:B28)","v":4.1333333333333347E-2},null,null,{"$f":"AVERAGE(E14:E28)","v":4.1200000000000007E-2},"What minus one does: 10/5 = 2, but 10/(5-1) = 2.5"]
["Year","Stock Return A","Deviation","Deviation ^2","Stock Return B","Deviation","Deviation ^2"]
[1995,0.05,{"$f":"B14-$B$12","v":8.6666666666666559E-3},{"$f":"C14^2","v":7.5111111111110919E-5},0.02,{"$f":"E14-$E$12","v":-2.1200000000000007E-2},{"$f":"F14^2","v":4.4944000000000028E-4}]
[1996,0.1,{"$f":"B15-$B$12","v":5.8666666666666659E-2},{"$f":"C15^2","v":3.4417777777777767E-3},0.04,{"$f":"E15-$E$12","v":-1.2000000000000066E-3},{"$f":"F15^2","v":1.4400000000000159E-6}]
[1997,0.12,7.8666666666666649E-2,6.1884444444444417E-3,3.5000000000000003E-2,-6.2000000000000041E-3,3.8440000000000052E-5]
[1998,0.17,0.12866666666666665,1.6555111111111107E-2,5.5E-2,1.3799999999999993E-2,1.9043999999999981E-4]
[1999,0.19,0.14866666666666667,2.2101777777777779E-2,0.04,-1.2000000000000066E-3,1.4400000000000159E-6]
[2000,0.01,-3.1333333333333345E-2,9.8177777777777846E-4,4.2000000000000003E-2,7.9999999999999516E-4,6.3999999999999228E-7]
[2001,-0.15,-0.19133333333333336,3.660844444444445E-2,4.2999999999999997E-2,1.7999999999999891E-3,3.2399999999999609E-6]
[2002,-0.03,-7.1333333333333346E-2,5.0884444444444467E-3,4.7E-2,5.7999999999999927E-3,3.3639999999999915E-5]
[2003,0.03,-1.1333333333333348E-2,1.2844444444444478E-4,0.05,8.7999999999999953E-3,7.7439999999999923E-5]
[2004,5.5E-2,1.3666666666666653E-2,1.8677777777777741E-4,5.0999999999999997E-2,9.7999999999999893E-3,9.6039999999999792E-5]
[2005,0.1,5.8666666666666659E-2,3.4417777777777767E-3,0.03,-1.1200000000000009E-2,1.2544000000000018E-4]
[2006,6.5000000000000002E-2,2.3666666666666655E-2,5.6011111111111062E-4,2.9000000000000001E-2,-1.2200000000000006E-2,1.4884000000000015E-4]
[2007,-0.02,-6.1333333333333351E-2,3.7617777777777801E-3,4.5999999999999999E-2,4.7999999999999918E-3,2.3039999999999922E-5]
[2008,-0.22,-0.26133333333333336,6.8295111111111126E-2,4.9000000000000002E-2,7.7999999999999944E-3,6.0839999999999912E-5]
[2009,0.15,0.10866666666666665,1.1808444444444441E-2,4.1000000000000002E-2,-2.0000000000000573E-4,4.000000000000229E-8]
[null,"Total",{"$f":"SUM(C14:C28)","v":-2.0816681711721685E-16},{"$f":"SUM(D14:D28)","v":0.17922333333333335},null,{"$f":"SUM(F14:F28)","v":-1.0408340855860843E-16},{"$f":"SUM(G14:G28)","v":1.2504E-3}]
[]
[null,"Sample Variance = s2",null,{"$f":"D29/B11","v":1.2801666666666668E-2},null,null,{"$f":"G29/E11","v":8.9314285714285719E-5},"Units are squared"]
[null,"Sample Standard Deviation = s",null,{"$f":"SQRT(D31)","v":0.11314445044573183},null,null,{"$f":"SQRT(G31)","v":9.4506235621934342E-3},"Square root to get back to same unit"]
[null,null,null,{"$f":"_xlfn.STDEV.S(B14:B28)","v":0.11314445044573183},null,null,{"$f":"_xlfn.STDEV.S(E14:E28)","v":9.4506235621933891E-3},"STDEV.S (Standard Deviation for Sample)"]
[null,null,null,null,null,null,null,"The sample SD, s, is a point estimator  of the population SD, sigma σ"]
[null,null,null,null,null,null,null,"s = Numerical Measure of Risk of Stock (Volitility)"]
[null,null,null,null,null,null,null,"Which mean more fairly represnets its data points?"]

{"sheet":"V(6)","index":62,"n_rows":14,"n_cols":5,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["Wage Data"]
[]
["Sample1","Sample2"]
[12,8]
[15,15]
[19,22]
[13,7]
[11,18.000000000000039]
[]
[null,"Sample1","Sample2"]
["Sample Variance = s^2",null,null,"VAR.S",{"$f":"\"In Excel you can use the function:\"&CHAR(10)&D11&CHAR(10)&\"for calculating \"&A11","v":"In Excel you can use the function:\nVAR.S\nfor calculating Sample Variance = s^2"}]
["Sample Standard Deviation =s",null,null,"STDEV.S",{"$f":"\"In Excel you can use the function:\"&CHAR(10)&D12&CHAR(10)&\"for calculating \"&A12","v":"In Excel you can use the function:\nSTDEV.S\nfor calculating Sample Standard Deviation =s"}]
["Population Variance = σ^2",null,null,"VAR.P",{"$f":"\"In Excel you can use the function:\"&CHAR(10)&D13&CHAR(10)&\"for calculating \"&A13","v":"In Excel you can use the function:\nVAR.P\nfor calculating Population Variance = σ^2"}]
["Population Standard Deviation = σ",null,null,"STDEV.P",{"$f":"\"In Excel you can use the function:\"&CHAR(10)&D14&CHAR(10)&\"for calculating \"&A14","v":"In Excel you can use the function:\nSTDEV.P\nfor calculating Population Standard Deviation = σ"}]

{"sheet":"V(6an)","index":63,"n_rows":14,"n_cols":5,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["Wage Data"]
[]
["Sample1","Sample2"]
[12,8]
[15,15]
[19,22]
[13,7]
[11,18.000000000000039]
[]
[null,"Sample1","Sample2"]
["Sample Variance = s^2",{"$f":"_xlfn.VAR.S(A4:A8)","v":10},{"$f":"_xlfn.VAR.S(B4:B8)","v":41.500000000000028},"VAR.S",{"$f":"\"In Excel you can use the function:\"&CHAR(10)&D11&CHAR(10)&\"for calculating \"&A11","v":"In Excel you can use the function:\nVAR.S\nfor calculating Sample Variance = s^2"}]
["Sample Standard Deviation =s",{"$f":"_xlfn.STDEV.S(A4:A8)","v":3.1622776601683795},{"$f":"_xlfn.STDEV.S(B4:B8)","v":6.4420493633625648},"STDEV.S",{"$f":"\"In Excel you can use the function:\"&CHAR(10)&D12&CHAR(10)&\"for calculating \"&A12","v":"In Excel you can use the function:\nSTDEV.S\nfor calculating Sample Standard Deviation =s"}]
["Population Variance = σ^2",{"$f":"VARP(A4:A8)","v":8},{"$f":"VARP(B4:B8)","v":33.200000000000038},"VAR.P",{"$f":"\"In Excel you can use the function:\"&CHAR(10)&D13&CHAR(10)&\"for calculating \"&A13","v":"In Excel you can use the function:\nVAR.P\nfor calculating Population Variance = σ^2"}]
["Population Standard Deviation = σ",{"$f":"STDEVP(A4:A8)","v":2.8284271247461903},{"$f":"STDEVP(B4:B8)","v":5.7619441163551768},"STDEV.P",{"$f":"\"In Excel you can use the function:\"&CHAR(10)&D14&CHAR(10)&\"for calculating \"&A14","v":"In Excel you can use the function:\nSTDEV.P\nfor calculating Population Standard Deviation = σ"}]

{"sheet":"CV","index":64,"n_rows":24,"n_cols":17,"rows_kept":24,"cut":false,"hidden":false,"merged":[[23,10,23,16],[12,0,12,6],[13,0,13,6],[14,0,14,6],[15,10,15,16],[22,10,22,16]]}
["Return on stock 1"," =",0.13]
["Standard deviation on\nhistorical returns stock 1"," =",0.2]
["Return on stock 2"," =",0.17]
["Standard deviation on\nhistorical returns stock 2"," =",0.33]
["Return on stock 3"," =",0.06]
["Standard deviation on\nhistorical returns stock 3"," =",0.08]
[]
["Coefficient of Variance"," =","s"," ÷","Xbar"," =","CV",null,{"$f":"E8&\"/\"&C8&\" = (for every one unit of dispersion (risk), how much return are you getting)\"","v":"Xbar/s = (for every one unit of dispersion (risk), how much return are you getting)"}]
["Coefficient of Variance for stock 1"," =",{"$f":"C2","v":0.2}," ÷",{"$f":"C1","v":0.13}," ="]
["Coefficient of Variance for stock 2"," =",{"$f":"C4","v":0.33}," ÷",{"$f":"C3","v":0.17}," ="]
["Coefficient of Variance for stock 3"," =",{"$f":"C6","v":0.08}," ÷",{"$f":"C5","v":0.06}," ="]
[]
["There is more dispersion relative to the mean for stock 2"]
["We can also say: For every 1% of return,\nwe have 1.94% standard deviation (proxy for risk)"]
["*Notice that we keep the units because there were\ndifferent units in the numerator & denominator"]
[null,null,null,null,null,null,null,null,null,null,"Compare Relative Variability (Dispersion) in Two Distributions"]
[]
[null,null,null,null,null,null,null,null,null,null,"Mean bonus paid per employee"," =",2000,null,"Mean years worked"," =",15]
[null,null,null,null,null,null,null,null,null,null,"Standard deviation"," =",755,null,"Standard deviation"," =",3]
[]
[null,null,null,null,null,null,null,null,null,null,"Coefficient of Variance"," =",null,null,"Coefficient of Variance"," ="]
[]
[null,null,null,null,null,null,null,null,null,null,"There is more variability relative to the mean in the distribution of bonus paid\ncompared with the distribution of years worked"]
[null,null,null,null,null,null,null,null,null,null,"*Notice here that the units cancel out"]

{"sheet":"CV (an)","index":65,"n_rows":24,"n_cols":17,"rows_kept":24,"cut":false,"hidden":false,"merged":[[23,10,23,16],[12,0,12,6],[13,0,13,6],[14,0,14,6],[15,10,15,16],[22,10,22,16]]}
["Return on stock 1"," =",0.13]
["Standard deviation on\nhistorical returns stock 1"," =",0.2]
["Return on stock 2"," =",0.17]
["Standard deviation on\nhistorical returns stock 2"," =",0.33]
["Return on stock 3"," =",0.06]
["Standard deviation on\nhistorical returns stock 3"," =",0.08]
[]
["Coefficient of Variance"," =","s"," ÷","Xbar"," =","CV",null,{"$f":"E8&\"/\"&C8&\" = (for every one unit of dispersion (risk), how much return are you getting)\"","v":"Xbar/s = (for every one unit of dispersion (risk), how much return are you getting)"}]
["Coefficient of Variance for stock 1"," =",{"$f":"C2","v":0.2}," ÷",{"$f":"C1","v":0.13}," =",{"$f":"C9/E9","v":1.5384615384615385},null,{"$f":"E9/C9","v":0.65}]
["Coefficient of Variance for stock 2"," =",{"$f":"C4","v":0.33}," ÷",{"$f":"C3","v":0.17}," =",{"$f":"C10/E10","v":1.9411764705882353},null,{"$f":"E10/C10","v":0.51515151515151514}]
["Coefficient of Variance for stock 3"," =",{"$f":"C6","v":0.08}," ÷",{"$f":"C5","v":0.06}," =",{"$f":"C11/E11","v":1.3333333333333335},null,{"$f":"E11/C11","v":0.75}]
[]
["There is more dispersion relative to the mean for stock 2"]
["We can also say: For every 1% of return,\nwe have 1.94% standard deviation (proxy for risk)"]
["*Notice that we keep the units because there were\ndifferent units in the numerator & denominator"]
[null,null,null,null,null,null,null,null,null,null,"Compare Relative Variability (Dispersion) in Two Distributions"]
[]
[null,null,null,null,null,null,null,null,null,null,"Mean bonus paid per employee"," =",2000,null,"Mean years worked"," =",15]
[null,null,null,null,null,null,null,null,null,null,"Standard deviation"," =",755,null,"Standard deviation"," =",3]
[]
[null,null,null,null,null,null,null,null,null,null,"Coefficient of Variance"," =",{"$f":"M19/M18","v":0.3775},null,"Coefficient of Variance"," =",{"$f":"Q19/Q18","v":0.2}]
[]
[null,null,null,null,null,null,null,null,null,null,"There is more variability relative to the mean in the distribution of bonus paid\ncompared with the distribution of years worked"]
[null,null,null,null,null,null,null,null,null,null,"*Notice here that the units cancel out"]

{"sheet":"DS","index":66,"n_rows":203,"n_cols":10,"rows_kept":203,"cut":false,"hidden":false,"merged":[]}
["Sample of 200 sales from www.boomerangs.com. Use Descriptive Statistics to reveal patterns in raw data."]
[]
["No.","Date (2010)","Customer Age","Coupon","Payment Method","Product (Boomerang Name)","Region","Price","Units","Sales"]
[1,"2010-05-22",21,"Coupon","Mastercard","Carlota","West",22.95,2,45.9]
[2,"2010-06-29",57,"Coupon","Mastercard","Yanaki","West",19.95,1,19.95]
[3,"2010-11-05",25,"No Coupon","Mastercard","Aspen","East",21.95,1,21.95]
[4,"2010-08-31",38,"No Coupon","American Express","Yanaki","West",19.95,1,19.95]
[5,"2010-05-30",22,"Coupon","Visa","Yanaki","West",19.95,4,79.8]
[6,"2010-10-05",29,"Coupon","PayPal","Yanaki","South",19.95,4,79.8]
[7,"2010-03-22",18,"Coupon","Visa","Yanaki","West",19.95,3,59.849999999999994]
[8,"2010-06-14",64,"No Coupon","Discover","Yanaki","West",19.95,7,139.65]
[9,"2010-05-09",27,"No Coupon","American Express","Yanaki","West",19.95,6,119.69999999999999]
[10,"2010-08-28",22,"No Coupon","Visa","Aspen","West",21.95,2,43.9]
[11,"2010-11-30",39,"Coupon","PayPal","Aspen","Mid West",21.95,2,43.9]
[12,"2010-09-13",61,"No Coupon","Mastercard","Yanaki","Mid West",19.95,5,99.75]
[13,"2010-10-23",18,"No Coupon","Visa","Carlota","Mid West",22.95,5,114.75]
[14,"2010-09-19",22,"No Coupon","PayPal","Carlota","West",22.95,4,91.8]
[15,"2010-09-20",52,"No Coupon","American Express","Carlota","Mid West",22.95,5,114.75]
[16,"2010-01-18",22,"Coupon","Visa","Carlota","West",22.95,1,22.95]
[17,"2010-07-28",18,"No Coupon","Discover","Sunset","West",24.95,5,124.75]
[18,"2010-06-06",55,"No Coupon","PayPal","Yanaki","South",19.95,1,19.95]
[19,"2010-01-30",20,"No Coupon","PayPal","Aspen","East",21.95,4,87.8]
[20,"2010-10-09",42,"Coupon","PayPal","Carlota","Mid West",22.95,1,22.95]
[21,"2010-07-04",30,"No Coupon","PayPal","Delicate Arch","South",29.95,10,299.5]
[22,"2010-11-08",64,"Coupon","Visa","Yanaki","Mid West",19.95,1,19.95]
[23,"2010-06-09",63,"Coupon","PayPal","Yanaki","Mid West",19.95,5,99.75]
[24,"2010-03-17",41,"Coupon","Mastercard","Yanaki","South",19.95,2,39.9]
[25,"2010-04-07",21,"No Coupon","Visa","Aspen","East",21.95,3,65.849999999999994]
[26,"2010-01-05",63,"No Coupon","PayPal","Sunset","East",24.95,1,24.95]
[27,"2010-07-22",54,"No Coupon","American Express","Aspen","West",21.95,1,21.95]
[28,"2010-11-12",18,"No Coupon","American Express","Yanaki","West",19.95,1,19.95]
[29,"2010-05-11",26,"No Coupon","Discover","Carlota","West",22.95,4,91.8]
[30,"2010-04-14",59,"No Coupon","PayPal","Aspen","Mid West",21.95,3,65.849999999999994]
[31,"2010-08-11",30,"No Coupon","Discover","Yanaki","West",19.95,2,39.9]
[32,"2010-11-14",64,"No Coupon","Visa","Aspen","West",21.95,2,43.9]
[33,"2010-01-21",30,"No Coupon","PayPal","Aspen","West",21.95,3,65.849999999999994]
[34,"2010-04-12",41,"Coupon","American Express","Aspen","West",21.95,2,43.9]
[35,"2010-06-04",23,"Coupon","Mastercard","Yanaki","South",19.95,5,99.75]
[36,"2010-10-19",52,"Coupon","Visa","Delicate Arch","West",29.95,1,29.95]
[37,"2010-09-07",18,"No Coupon","PayPal","Aspen","West",21.95,3,65.849999999999994]
[38,"2010-09-19",32,"No Coupon","PayPal","Carlota","West",22.95,1,22.95]
[39,"2010-01-17",22,"Coupon","American Express","Yanaki","Mid West",19.95,1,19.95]
[40,"2010-03-15",29,"Coupon","PayPal","Yanaki","South",19.95,5,99.75]
[41,"2010-12-16",25,"No Coupon","Mastercard","Bellen","Mid West",24.95,5,124.75]
[42,"2010-07-08",63,"No Coupon","PayPal","Aspen","West",21.95,1,21.95]
[43,"2010-05-13",26,"No Coupon","Mastercard","Sunset","Mid West",24.95,7,174.65]
[44,"2010-03-03",31,"Coupon","Discover","Delicate Arch","West",29.95,1,29.95]
[45,"2010-04-30",23,"No Coupon","PayPal","Delicate Arch","Mid West",29.95,5,149.75]
[46,"2010-07-11",42,"Coupon","PayPal","Delicate Arch","Mid West",29.95,1,29.95]
[47,"2010-03-22",28,"Coupon","Visa","Carlota","East",22.95,2,45.9]
[48,"2010-08-27",23,"No Coupon","Visa","Carlota","West",22.95,7,160.65]
[49,"2010-11-16",19,"No Coupon","Mastercard","Carlota","Mid West",22.95,7,160.65]
[50,"2010-01-26",37,"Coupon","Visa","Yanaki","West",19.95,6,119.69999999999999]
[51,"2010-05-06",38,"No Coupon","Mastercard","Aspen","East",21.95,2,43.9]
[52,"2010-03-18",50,"Coupon","Mastercard","Yanaki","Mid West",19.95,6,119.69999999999999]
[53,"2010-04-16",26,"No Coupon","Discover","Aspen","West",21.95,3,65.849999999999994]
[54,"2010-01-05",33,"No Coupon","PayPal","Carlota","South",22.95,1,22.95]
[55,"2010-11-09",59,"No Coupon","PayPal","Aspen","Mid West",21.95,3,65.849999999999994]
[56,"2010-07-29",32,"No Coupon","Visa","Aspen","Mid West",21.95,5,109.75]
[57,"2010-12-07",27,"No Coupon","Visa","Carlota","Mid West",22.95,5,114.75]
[58,"2010-11-22",54,"Coupon","American Express","Bellen","West",24.95,10,249.5]
[59,"2010-01-10",63,"No Coupon","PayPal","Aspen","West",21.95,5,109.75]
[60,"2010-06-01",48,"No Coupon","Visa","Carlota","East",22.95,5,114.75]
[61,"2010-05-02",29,"No Coupon","American Express","Carlota","East",22.95,5,114.75]
[62,"2010-06-13",38,"Coupon","Visa","Delicate Arch","West",29.95,4,119.8]
[63,"2010-02-16",24,"Coupon","Mastercard","Delicate Arch","East",29.95,1,29.95]
[64,"2010-08-02",51,"No Coupon","Visa","Carlota","West",22.95,5,114.75]
[65,"2010-11-01",25,"Coupon","Mastercard","Delicate Arch","West",29.95,7,209.65]
[66,"2010-11-08",65,"No Coupon","Visa","Carlota","West",22.95,5,114.75]
[67,"2010-08-17",35,"No Coupon","PayPal","Yanaki","Mid West",19.95,3,59.849999999999994]
[68,"2010-09-27",35,"No Coupon","Mastercard","Sunset","East",24.95,5,124.75]
[69,"2010-01-09",21,"No Coupon","Visa","Yanaki","Mid West",19.95,2,39.9]
[70,"2010-10-10",47,"No Coupon","Mastercard","Sunset","West",24.95,5,124.75]
[71,"2010-12-31",62,"No Coupon","Discover","Sunset","East",24.95,1,24.95]
[72,"2010-12-06",63,"No Coupon","PayPal","Carlota","East",22.95,1,22.95]
[73,"2010-03-18",23,"No Coupon","American Express","Bellen","Mid West",24.95,10,249.5]
[74,"2010-03-22",59,"No Coupon","Visa","Yanaki","South",19.95,3,59.849999999999994]
[75,"2010-09-14",48,"Coupon","Visa","Aspen","West",21.95,2,43.9]
[76,"2010-02-09",57,"No Coupon","Mastercard","Yanaki","South",19.95,1,19.95]
[77,"2010-03-24",19,"No Coupon","Discover","Delicate Arch","Mid West",29.95,1,29.95]
[78,"2010-07-28",48,"Coupon","Mastercard","Yanaki","Mid West",19.95,1,19.95]
[79,"2010-08-26",21,"Coupon","Mastercard","Aspen","South",21.95,3,65.849999999999994]
[80,"2010-03-05",40,"No Coupon","American Express","Carlota","West",22.95,1,22.95]
[81,"2010-08-18",25,"No Coupon","Visa","Yanaki","Mid West",19.95,4,79.8]
[82,"2010-11-02",59,"Coupon","Mastercard","Yanaki","South",19.95,4,79.8]
[83,"2010-12-19",57,"No Coupon","Visa","Carlota","West",22.95,5,114.75]
[84,"2010-07-05",56,"Coupon","Discover","Carlota","West",22.95,1,22.95]
[85,"2010-04-16",19,"No Coupon","Visa","Yanaki","West",19.95,1,19.95]
[86,"2010-12-23",54,"No Coupon","Visa","Aspen","Mid West",21.95,5,109.75]
[87,"2010-05-29",65,"No Coupon","PayPal","Delicate Arch","Mid West",29.95,2,59.9]
[88,"2010-05-01",25,"Coupon","PayPal","Aspen","West",21.95,2,43.9]
[89,"2010-07-03",30,"No Coupon","American Express","Yanaki","West",19.95,2,39.9]
[90,"2010-08-12",57,"No Coupon","Mastercard","Delicate Arch","West",29.95,7,209.65]
[91,"2010-06-21",43,"Coupon","PayPal","Yanaki","West",19.95,1,19.95]
[92,"2010-12-15",44,"No Coupon","Mastercard","Yanaki","South",19.95,4,79.8]
[93,"2010-05-25",21,"No Coupon","PayPal","Bellen","East",24.95,5,124.75]
[94,"2010-03-23",20,"No Coupon","PayPal","Bellen","West",24.95,1,24.95]
[95,"2010-01-22",49,"Coupon","Visa","Carlota","West",22.95,7,160.65]
[96,"2010-09-26",37,"No Coupon","Mastercard","Aspen","South",21.95,3,65.849999999999994]
[97,"2010-12-27",26,"No Coupon","PayPal","Carlota","West",22.95,6,137.69999999999999]
[98,"2010-07-24",62,"No Coupon","Mastercard","Delicate Arch","East",29.95,1,29.95]
[99,"2010-04-27",38,"No Coupon","PayPal","Yanaki","West",19.95,6,119.69999999999999]
[100,"2010-05-07",55,"No Coupon","Visa","Yanaki","West",19.95,1,19.95]
[101,"2010-03-03",24,"Coupon","American Express","Yanaki","East",19.95,2,39.9]
[102,"2010-03-23",30,"No Coupon","PayPal","Carlota","Mid West",22.95,5,114.75]
[103,"2010-12-05",39,"Coupon","Visa","Aspen","Mid West",21.95,1,21.95]
[104,"2010-11-11",59,"Coupon","PayPal","Delicate Arch","South",29.95,6,179.7]
[105,"2010-04-13",26,"No Coupon","Discover","Yanaki","East",19.95,2,39.9]
[106,"2010-12-13",33,"No Coupon","Visa","Sunset","Mid West",24.95,1,24.95]
[107,"2010-10-05",20,"No Coupon","Visa","Bellen","West",24.95,4,99.8]
[108,"2010-01-02",18,"No Coupon","Visa","Aspen","West",21.95,4,87.8]
[109,"2010-11-04",19,"Coupon","PayPal","Yanaki","East",19.95,2,39.9]
[110,"2010-04-29",61,"No Coupon","PayPal","Aspen","West",21.95,3,65.849999999999994]
[111,"2010-10-02",39,"Coupon","PayPal","Yanaki","East",19.95,10,199.5]
[112,"2010-12-26",52,"Coupon","Discover","Aspen","West",21.95,1,21.95]
[113,"2010-11-05",20,"No Coupon","Visa","Sunset","West",24.95,5,124.75]
[114,"2010-11-15",50,"No Coupon","Visa","Delicate Arch","West",29.95,1,29.95]
[115,"2010-06-27",29,"Coupon","PayPal","Aspen","South",21.95,1,21.95]
[116,"2010-04-21",55,"No Coupon","Visa","Delicate Arch","West",29.95,4,119.8]
[117,"2010-09-25",18,"No Coupon","American Express","Delicate Arch","West",29.95,3,89.85]
[118,"2010-01-24",39,"Coupon","Mastercard","Aspen","Mid West",21.95,3,65.849999999999994]
[119,"2010-01-04",35,"No Coupon","Visa","Carlota","South",22.95,4,91.8]
[120,"2010-05-06",38,"Coupon","American Express","Bellen","South",24.95,6,149.69999999999999]
[121,"2010-06-22",20,"No Coupon","Visa","Yanaki","East",19.95,3,59.849999999999994]
[122,"2010-07-12",60,"No Coupon","Discover","Aspen","Mid West",21.95,6,131.69999999999999]
[123,"2010-05-03",61,"No Coupon","Visa","Sunset","Mid West",24.95,2,49.9]
[124,"2010-03-09",62,"Coupon","PayPal","Aspen","West",21.95,2,43.9]
[125,"2010-03-02",21,"No Coupon","Visa","Yanaki","Mid West",19.95,1,19.95]
[126,"2010-03-28",40,"No Coupon","Discover","Aspen","South",21.95,1,21.95]
[127,"2010-01-15",25,"No Coupon","Visa","Bellen","West",24.95,1,24.95]
[128,"2010-11-18",50,"No Coupon","Mastercard","Yanaki","West",19.95,2,39.9]
[129,"2010-03-27",24,"No Coupon","Visa","Bellen","West",24.95,1,24.95]
[130,"2010-08-11",28,"Coupon","PayPal","Carlota","West",22.95,5,114.75]
[131,"2010-12-24",22,"No Coupon","Visa","Yanaki","Mid West",19.95,6,119.69999999999999]
[132,"2010-11-27",22,"No Coupon","PayPal","Aspen","West",21.95,2,43.9]
[133,"2010-03-12",27,"No Coupon","Visa","Bellen","West",24.95,1,24.95]
[134,"2010-09-16",54,"Coupon","Visa","Sunset","West",24.95,7,174.65]
[135,"2010-02-01",25,"No Coupon","Mastercard","Bellen","West",24.95,1,24.95]
[136,"2010-07-03",25,"No Coupon","Visa","Sunset","Mid West",24.95,2,49.9]
[137,"2010-08-30",30,"No Coupon","PayPal","Yanaki","East",19.95,1,19.95]
[138,"2010-09-18",59,"Coupon","Mastercard","Yanaki","South",19.95,2,39.9]
[139,"2010-11-24",51,"No Coupon","Visa","Carlota","West",22.95,2,45.9]
[140,"2010-12-22",38,"No Coupon","Visa","Delicate Arch","West",29.95,6,179.7]
[141,"2010-04-23",28,"No Coupon","PayPal","Carlota","South",22.95,7,160.65]
[142,"2010-11-18",30,"Coupon","Discover","Aspen","West",21.95,1,21.95]
[143,"2010-10-28",43,"No Coupon","Visa","Bellen","South",24.95,5,124.75]
[144,"2010-08-14",42,"No Coupon","PayPal","Delicate Arch","West",29.95,3,89.85]
[145,"2010-05-05",24,"No Coupon","Visa","Bellen","Mid West",24.95,2,49.9]
[146,"2010-08-25",47,"Coupon","Visa","Carlota","Mid West",22.95,1,22.95]
[147,"2010-10-25",23,"No Coupon","PayPal","Yanaki","Mid West",19.95,1,19.95]
[148,"2010-07-31",59,"No Coupon","PayPal","Yanaki","East",19.95,5,99.75]
[149,"2010-07-25",22,"Coupon","Mastercard","Carlota","West",22.95,4,91.8]
[150,"2010-09-30",27,"Coupon","Visa","Bellen","Mid West",24.95,2,49.9]
[151,"2010-10-03",65,"No Coupon","Discover","Aspen","East",21.95,1,21.95]
[152,"2010-04-01",27,"No Coupon","Mastercard","Carlota","Mid West",22.95,2,45.9]
[153,"2010-12-15",27,"No Coupon","American Express","Carlota","East",22.95,1,22.95]
[154,"2010-01-07",28,"No Coupon","PayPal","Carlota","West",22.95,2,45.9]
[155,"2010-07-23",22,"Coupon","PayPal","Bellen","West",24.95,1,24.95]
[156,"2010-03-16",42,"No Coupon","PayPal","Yanaki","East",19.95,2,39.9]
[157,"2010-12-04",25,"No Coupon","American Express","Delicate Arch","East",29.95,6,179.7]
[158,"2010-01-08",41,"Coupon","Mastercard","Aspen","West",21.95,1,21.95]
[159,"2010-06-02",46,"Coupon","PayPal","Bellen","West",24.95,1,24.95]
[160,"2010-08-18",41,"No Coupon","Discover","Sunset","West",24.95,3,74.849999999999994]
[161,"2010-04-24",29,"No Coupon","Mastercard","Yanaki","West",19.95,4,79.8]
[162,"2010-12-01",50,"No Coupon","Visa","Yanaki","Mid West",19.95,1,19.95]
[163,"2010-12-31",50,"Coupon","Visa","Carlota","Mid West",22.95,1,22.95]
[164,"2010-04-30",34,"Coupon","PayPal","Carlota","Mid West",22.95,2,45.9]
[165,"2010-03-16",24,"Coupon","American Express","Aspen","West",21.95,3,65.849999999999994]
[166,"2010-01-28",29,"No Coupon","Mastercard","Yanaki","West",19.95,7,139.65]
[167,"2010-08-03",35,"No Coupon","Mastercard","Carlota","Mid West",22.95,1,22.95]
[168,"2010-11-11",24,"No Coupon","Visa","Yanaki","West",19.95,2,39.9]
[169,"2010-12-13",23,"Coupon","Visa","Aspen","South",21.95,5,109.75]
[170,"2010-03-27",31,"No Coupon","PayPal","Carlota","Mid West",22.95,7,160.65]
[171,"2010-10-08",24,"Coupon","PayPal","Bellen","Mid West",24.95,2,49.9]
[172,"2010-08-03",30,"No Coupon","Visa","Carlota","Mid West",22.95,1,22.95]
[173,"2010-03-10",22,"Coupon","Visa","Carlota","West",22.95,2,45.9]
[174,"2010-03-02",43,"No Coupon","Visa","Carlota","East",22.95,3,68.849999999999994]
[175,"2010-01-26",55,"No Coupon","Visa","Carlota","West",22.95,10,229.5]
[176,"2010-05-06",38,"No Coupon","American Express","Delicate Arch","West",29.95,1,29.95]
[177,"2010-03-10",28,"Coupon","Visa","Yanaki","West",19.95,2,39.9]
[178,"2010-11-18",30,"Coupon","PayPal","Aspen","Mid West",21.95,2,43.9]
[179,"2010-01-30",35,"Coupon","Discover","Yanaki","West",19.95,1,19.95]
[180,"2010-07-02",41,"No Coupon","Visa","Delicate Arch","West",29.95,2,59.9]
[181,"2010-10-13",28,"Coupon","Discover","Yanaki","East",19.95,5,99.75]
[182,"2010-02-07",65,"No Coupon","Discover","Bellen","Mid West",24.95,7,174.65]
[183,"2010-06-05",20,"No Coupon","Mastercard","Aspen","West",21.95,3,65.849999999999994]
[184,"2010-11-02",39,"No Coupon","Visa","Sunset","Mid West",24.95,5,124.75]
[185,"2010-12-13",19,"No Coupon","Visa","Aspen","East",21.95,4,87.8]
[186,"2010-10-23",64,"No Coupon","Visa","Carlota","West",22.95,10,229.5]
[187,"2010-12-22",42,"Coupon","PayPal","Yanaki","South",19.95,5,99.75]
[188,"2010-08-21",24,"Coupon","PayPal","Yanaki","Mid West",19.95,1,19.95]
[189,"2010-08-28",24,"Coupon","PayPal","Yanaki","Mid West",19.95,1,19.95]
[190,"2010-06-20",18,"No Coupon","American Express","Bellen","Mid West",24.95,4,99.8]
[191,"2010-04-30",36,"Coupon","Mastercard","Bellen","East",24.95,1,24.95]
[192,"2010-10-14",61,"No Coupon","Mastercard","Carlota","Mid West",22.95,5,114.75]
[193,"2010-08-04",22,"No Coupon","Visa","Yanaki","West",19.95,3,59.849999999999994]
[194,"2010-10-28",55,"Coupon","PayPal","Aspen","West",21.95,2,43.9]
[195,"2010-11-04",27,"No Coupon","American Express","Sunset","West",24.95,3,74.849999999999994]
[196,"2010-01-05",49,"No Coupon","PayPal","Yanaki","Mid West",19.95,1,19.95]
[197,"2010-12-11",29,"Coupon","Visa","Carlota","West",22.95,1,22.95]
[198,"2010-07-18",33,"No Coupon","PayPal","Aspen","West",21.95,7,153.65]
[199,"2010-05-31",52,"No Coupon","Visa","Yanaki","West",19.95,2,39.9]
[200,"2010-12-16",26,"Coupon","PayPal","Aspen","West",21.95,6,131.69999999999999]

{"sheet":"DS (an)","index":67,"n_rows":203,"n_cols":13,"rows_kept":203,"cut":false,"hidden":false,"merged":[]}
["Sample of 200 sales from www.boomerangs.com. Use Descriptive Statistics to reveal patterns in raw data.",null,null,null,null,null,null,null,null,null,null,"Sales"]
[]
["No.","Date (2010)","Customer Age","Coupon","Payment Method","Product (Boomerang Name)","Region","Price","Units","Sales",null,"Mean",75.057750000000041]
[1,"2010-05-22",21,"Coupon","Mastercard","Carlota","West",22.95,2,45.9,null,"Standard Error",3.9247905890668311]
[2,"2010-06-29",57,"Coupon","Mastercard","Yanaki","West",19.95,1,19.95,null,"Median",59.849999999999994]
[3,"2010-11-05",25,"No Coupon","Mastercard","Aspen","East",21.95,1,21.95,null,"Mode",19.95]
[4,"2010-08-31",38,"No Coupon","American Express","Yanaki","West",19.95,1,19.95,null,"Standard Deviation",55.504920805326016]
[5,"2010-05-30",22,"Coupon","Visa","Yanaki","West",19.95,4,79.8,null,"Sample Variance",3080.7962336055125]
[6,"2010-10-05",29,"Coupon","PayPal","Yanaki","South",19.95,4,79.8,null,"Kurtosis",1.3861851155914824]
[7,"2010-03-22",18,"Coupon","Visa","Yanaki","West",19.95,3,59.849999999999994,null,"Skewness",1.2141941767956757]
[8,"2010-06-14",64,"No Coupon","Discover","Yanaki","West",19.95,7,139.65,null,"Range",279.55]
[9,"2010-05-09",27,"No Coupon","American Express","Yanaki","West",19.95,6,119.69999999999999,null,"Minimum",19.95]
[10,"2010-08-28",22,"No Coupon","Visa","Aspen","West",21.95,2,43.9,null,"Maximum",299.5]
[11,"2010-11-30",39,"Coupon","PayPal","Aspen","Mid West",21.95,2,43.9,null,"Sum",15011.550000000008]
[12,"2010-09-13",61,"No Coupon","Mastercard","Yanaki","Mid West",19.95,5,99.75,null,"Count",200]
[13,"2010-10-23",18,"No Coupon","Visa","Carlota","Mid West",22.95,5,114.75]
[14,"2010-09-19",22,"No Coupon","PayPal","Carlota","West",22.95,4,91.8]
[15,"2010-09-20",52,"No Coupon","American Express","Carlota","Mid West",22.95,5,114.75]
[16,"2010-01-18",22,"Coupon","Visa","Carlota","West",22.95,1,22.95]
[17,"2010-07-28",18,"No Coupon","Discover","Sunset","West",24.95,5,124.75]
[18,"2010-06-06",55,"No Coupon","PayPal","Yanaki","South",19.95,1,19.95]
[19,"2010-01-30",20,"No Coupon","PayPal","Aspen","East",21.95,4,87.8]
[20,"2010-10-09",42,"Coupon","PayPal","Carlota","Mid West",22.95,1,22.95]
[21,"2010-07-04",30,"No Coupon","PayPal","Delicate Arch","South",29.95,10,299.5]
[22,"2010-11-08",64,"Coupon","Visa","Yanaki","Mid West",19.95,1,19.95]
[23,"2010-06-09",63,"Coupon","PayPal","Yanaki","Mid West",19.95,5,99.75]
[24,"2010-03-17",41,"Coupon","Mastercard","Yanaki","South",19.95,2,39.9]
[25,"2010-04-07",21,"No Coupon","Visa","Aspen","East",21.95,3,65.849999999999994]
[26,"2010-01-05",63,"No Coupon","PayPal","Sunset","East",24.95,1,24.95]
[27,"2010-07-22",54,"No Coupon","American Express","Aspen","West",21.95,1,21.95]
[28,"2010-11-12",18,"No Coupon","American Express","Yanaki","West",19.95,1,19.95]
[29,"2010-05-11",26,"No Coupon","Discover","Carlota","West",22.95,4,91.8]
[30,"2010-04-14",59,"No Coupon","PayPal","Aspen","Mid West",21.95,3,65.849999999999994]
[31,"2010-08-11",30,"No Coupon","Discover","Yanaki","West",19.95,2,39.9]
[32,"2010-11-14",64,"No Coupon","Visa","Aspen","West",21.95,2,43.9]
[33,"2010-01-21",30,"No Coupon","PayPal","Aspen","West",21.95,3,65.849999999999994]
[34,"2010-04-12",41,"Coupon","American Express","Aspen","West",21.95,2,43.9]
[35,"2010-06-04",23,"Coupon","Mastercard","Yanaki","South",19.95,5,99.75]
[36,"2010-10-19",52,"Coupon","Visa","Delicate Arch","West",29.95,1,29.95]
[37,"2010-09-07",18,"No Coupon","PayPal","Aspen","West",21.95,3,65.849999999999994]
[38,"2010-09-19",32,"No Coupon","PayPal","Carlota","West",22.95,1,22.95]
[39,"2010-01-17",22,"Coupon","American Express","Yanaki","Mid West",19.95,1,19.95]
[40,"2010-03-15",29,"Coupon","PayPal","Yanaki","South",19.95,5,99.75]
[41,"2010-12-16",25,"No Coupon","Mastercard","Bellen","Mid West",24.95,5,124.75]
[42,"2010-07-08",63,"No Coupon","PayPal","Aspen","West",21.95,1,21.95]
[43,"2010-05-13",26,"No Coupon","Mastercard","Sunset","Mid West",24.95,7,174.65]
[44,"2010-03-03",31,"Coupon","Discover","Delicate Arch","West",29.95,1,29.95]
[45,"2010-04-30",23,"No Coupon","PayPal","Delicate Arch","Mid West",29.95,5,149.75]
[46,"2010-07-11",42,"Coupon","PayPal","Delicate Arch","Mid West",29.95,1,29.95]
[47,"2010-03-22",28,"Coupon","Visa","Carlota","East",22.95,2,45.9]
[48,"2010-08-27",23,"No Coupon","Visa","Carlota","West",22.95,7,160.65]
[49,"2010-11-16",19,"No Coupon","Mastercard","Carlota","Mid West",22.95,7,160.65]
[50,"2010-01-26",37,"Coupon","Visa","Yanaki","West",19.95,6,119.69999999999999]
[51,"2010-05-06",38,"No Coupon","Mastercard","Aspen","East",21.95,2,43.9]
[52,"2010-03-18",50,"Coupon","Mastercard","Yanaki","Mid West",19.95,6,119.69999999999999]
[53,"2010-04-16",26,"No Coupon","Discover","Aspen","West",21.95,3,65.849999999999994]
[54,"2010-01-05",33,"No Coupon","PayPal","Carlota","South",22.95,1,22.95]
[55,"2010-11-09",59,"No Coupon","PayPal","Aspen","Mid West",21.95,3,65.849999999999994]
[56,"2010-07-29",32,"No Coupon","Visa","Aspen","Mid West",21.95,5,109.75]
[57,"2010-12-07",27,"No Coupon","Visa","Carlota","Mid West",22.95,5,114.75]
[58,"2010-11-22",54,"Coupon","American Express","Bellen","West",24.95,10,249.5]
[59,"2010-01-10",63,"No Coupon","PayPal","Aspen","West",21.95,5,109.75]
[60,"2010-06-01",48,"No Coupon","Visa","Carlota","East",22.95,5,114.75]
[61,"2010-05-02",29,"No Coupon","American Express","Carlota","East",22.95,5,114.75]
[62,"2010-06-13",38,"Coupon","Visa","Delicate Arch","West",29.95,4,119.8]
[63,"2010-02-16",24,"Coupon","Mastercard","Delicate Arch","East",29.95,1,29.95]
[64,"2010-08-02",51,"No Coupon","Visa","Carlota","West",22.95,5,114.75]
[65,"2010-11-01",25,"Coupon","Mastercard","Delicate Arch","West",29.95,7,209.65]
[66,"2010-11-08",65,"No Coupon","Visa","Carlota","West",22.95,5,114.75]
[67,"2010-08-17",35,"No Coupon","PayPal","Yanaki","Mid West",19.95,3,59.849999999999994]
[68,"2010-09-27",35,"No Coupon","Mastercard","Sunset","East",24.95,5,124.75]
[69,"2010-01-09",21,"No Coupon","Visa","Yanaki","Mid West",19.95,2,39.9]
[70,"2010-10-10",47,"No Coupon","Mastercard","Sunset","West",24.95,5,124.75]
[71,"2010-12-31",62,"No Coupon","Discover","Sunset","East",24.95,1,24.95]
[72,"2010-12-06",63,"No Coupon","PayPal","Carlota","East",22.95,1,22.95]
[73,"2010-03-18",23,"No Coupon","American Express","Bellen","Mid West",24.95,10,249.5]
[74,"2010-03-22",59,"No Coupon","Visa","Yanaki","South",19.95,3,59.849999999999994]
[75,"2010-09-14",48,"Coupon","Visa","Aspen","West",21.95,2,43.9]
[76,"2010-02-09",57,"No Coupon","Mastercard","Yanaki","South",19.95,1,19.95]
[77,"2010-03-24",19,"No Coupon","Discover","Delicate Arch","Mid West",29.95,1,29.95]
[78,"2010-07-28",48,"Coupon","Mastercard","Yanaki","Mid West",19.95,1,19.95]
[79,"2010-08-26",21,"Coupon","Mastercard","Aspen","South",21.95,3,65.849999999999994]
[80,"2010-03-05",40,"No Coupon","American Express","Carlota","West",22.95,1,22.95]
[81,"2010-08-18",25,"No Coupon","Visa","Yanaki","Mid West",19.95,4,79.8]
[82,"2010-11-02",59,"Coupon","Mastercard","Yanaki","South",19.95,4,79.8]
[83,"2010-12-19",57,"No Coupon","Visa","Carlota","West",22.95,5,114.75]
[84,"2010-07-05",56,"Coupon","Discover","Carlota","West",22.95,1,22.95]
[85,"2010-04-16",19,"No Coupon","Visa","Yanaki","West",19.95,1,19.95]
[86,"2010-12-23",54,"No Coupon","Visa","Aspen","Mid West",21.95,5,109.75]
[87,"2010-05-29",65,"No Coupon","PayPal","Delicate Arch","Mid West",29.95,2,59.9]
[88,"2010-05-01",25,"Coupon","PayPal","Aspen","West",21.95,2,43.9]
[89,"2010-07-03",30,"No Coupon","American Express","Yanaki","West",19.95,2,39.9]
[90,"2010-08-12",57,"No Coupon","Mastercard","Delicate Arch","West",29.95,7,209.65]
[91,"2010-06-21",43,"Coupon","PayPal","Yanaki","West",19.95,1,19.95]
[92,"2010-12-15",44,"No Coupon","Mastercard","Yanaki","South",19.95,4,79.8]
[93,"2010-05-25",21,"No Coupon","PayPal","Bellen","East",24.95,5,124.75]
[94,"2010-03-23",20,"No Coupon","PayPal","Bellen","West",24.95,1,24.95]
[95,"2010-01-22",49,"Coupon","Visa","Carlota","West",22.95,7,160.65]
[96,"2010-09-26",37,"No Coupon","Mastercard","Aspen","South",21.95,3,65.849999999999994]
[97,"2010-12-27",26,"No Coupon","PayPal","Carlota","West",22.95,6,137.69999999999999]
[98,"2010-07-24",62,"No Coupon","Mastercard","Delicate Arch","East",29.95,1,29.95]
[99,"2010-04-27",38,"No Coupon","PayPal","Yanaki","West",19.95,6,119.69999999999999]
[100,"2010-05-07",55,"No Coupon","Visa","Yanaki","West",19.95,1,19.95]
[101,"2010-03-03",24,"Coupon","American Express","Yanaki","East",19.95,2,39.9]
[102,"2010-03-23",30,"No Coupon","PayPal","Carlota","Mid West",22.95,5,114.75]
[103,"2010-12-05",39,"Coupon","Visa","Aspen","Mid West",21.95,1,21.95]
[104,"2010-11-11",59,"Coupon","PayPal","Delicate Arch","South",29.95,6,179.7]
[105,"2010-04-13",26,"No Coupon","Discover","Yanaki","East",19.95,2,39.9]
[106,"2010-12-13",33,"No Coupon","Visa","Sunset","Mid West",24.95,1,24.95]
[107,"2010-10-05",20,"No Coupon","Visa","Bellen","West",24.95,4,99.8]
[108,"2010-01-02",18,"No Coupon","Visa","Aspen","West",21.95,4,87.8]
[109,"2010-11-04",19,"Coupon","PayPal","Yanaki","East",19.95,2,39.9]
[110,"2010-04-29",61,"No Coupon","PayPal","Aspen","West",21.95,3,65.849999999999994]
[111,"2010-10-02",39,"Coupon","PayPal","Yanaki","East",19.95,10,199.5]
[112,"2010-12-26",52,"Coupon","Discover","Aspen","West",21.95,1,21.95]
[113,"2010-11-05",20,"No Coupon","Visa","Sunset","West",24.95,5,124.75]
[114,"2010-11-15",50,"No Coupon","Visa","Delicate Arch","West",29.95,1,29.95]
[115,"2010-06-27",29,"Coupon","PayPal","Aspen","South",21.95,1,21.95]
[116,"2010-04-21",55,"No Coupon","Visa","Delicate Arch","West",29.95,4,119.8]
[117,"2010-09-25",18,"No Coupon","American Express","Delicate Arch","West",29.95,3,89.85]
[118,"2010-01-24",39,"Coupon","Mastercard","Aspen","Mid West",21.95,3,65.849999999999994]
[119,"2010-01-04",35,"No Coupon","Visa","Carlota","South",22.95,4,91.8]
[120,"2010-05-06",38,"Coupon","American Express","Bellen","South",24.95,6,149.69999999999999]
[121,"2010-06-22",20,"No Coupon","Visa","Yanaki","East",19.95,3,59.849999999999994]
[122,"2010-07-12",60,"No Coupon","Discover","Aspen","Mid West",21.95,6,131.69999999999999]
[123,"2010-05-03",61,"No Coupon","Visa","Sunset","Mid West",24.95,2,49.9]
[124,"2010-03-09",62,"Coupon","PayPal","Aspen","West",21.95,2,43.9]
[125,"2010-03-02",21,"No Coupon","Visa","Yanaki","Mid West",19.95,1,19.95]
[126,"2010-03-28",40,"No Coupon","Discover","Aspen","South",21.95,1,21.95]
[127,"2010-01-15",25,"No Coupon","Visa","Bellen","West",24.95,1,24.95]
[128,"2010-11-18",50,"No Coupon","Mastercard","Yanaki","West",19.95,2,39.9]
[129,"2010-03-27",24,"No Coupon","Visa","Bellen","West",24.95,1,24.95]
[130,"2010-08-11",28,"Coupon","PayPal","Carlota","West",22.95,5,114.75]
[131,"2010-12-24",22,"No Coupon","Visa","Yanaki","Mid West",19.95,6,119.69999999999999]
[132,"2010-11-27",22,"No Coupon","PayPal","Aspen","West",21.95,2,43.9]
[133,"2010-03-12",27,"No Coupon","Visa","Bellen","West",24.95,1,24.95]
[134,"2010-09-16",54,"Coupon","Visa","Sunset","West",24.95,7,174.65]
[135,"2010-02-01",25,"No Coupon","Mastercard","Bellen","West",24.95,1,24.95]
[136,"2010-07-03",25,"No Coupon","Visa","Sunset","Mid West",24.95,2,49.9]
[137,"2010-08-30",30,"No Coupon","PayPal","Yanaki","East",19.95,1,19.95]
[138,"2010-09-18",59,"Coupon","Mastercard","Yanaki","South",19.95,2,39.9]
[139,"2010-11-24",51,"No Coupon","Visa","Carlota","West",22.95,2,45.9]
[140,"2010-12-22",38,"No Coupon","Visa","Delicate Arch","West",29.95,6,179.7]
[141,"2010-04-23",28,"No Coupon","PayPal","Carlota","South",22.95,7,160.65]
[142,"2010-11-18",30,"Coupon","Discover","Aspen","West",21.95,1,21.95]
[143,"2010-10-28",43,"No Coupon","Visa","Bellen","South",24.95,5,124.75]
[144,"2010-08-14",42,"No Coupon","PayPal","Delicate Arch","West",29.95,3,89.85]
[145,"2010-05-05",24,"No Coupon","Visa","Bellen","Mid West",24.95,2,49.9]
[146,"2010-08-25",47,"Coupon","Visa","Carlota","Mid West",22.95,1,22.95]
[147,"2010-10-25",23,"No Coupon","PayPal","Yanaki","Mid West",19.95,1,19.95]
[148,"2010-07-31",59,"No Coupon","PayPal","Yanaki","East",19.95,5,99.75]
[149,"2010-07-25",22,"Coupon","Mastercard","Carlota","West",22.95,4,91.8]
[150,"2010-09-30",27,"Coupon","Visa","Bellen","Mid West",24.95,2,49.9]
[151,"2010-10-03",65,"No Coupon","Discover","Aspen","East",21.95,1,21.95]
[152,"2010-04-01",27,"No Coupon","Mastercard","Carlota","Mid West",22.95,2,45.9]
[153,"2010-12-15",27,"No Coupon","American Express","Carlota","East",22.95,1,22.95]
[154,"2010-01-07",28,"No Coupon","PayPal","Carlota","West",22.95,2,45.9]
[155,"2010-07-23",22,"Coupon","PayPal","Bellen","West",24.95,1,24.95]
[156,"2010-03-16",42,"No Coupon","PayPal","Yanaki","East",19.95,2,39.9]
[157,"2010-12-04",25,"No Coupon","American Express","Delicate Arch","East",29.95,6,179.7]
[158,"2010-01-08",41,"Coupon","Mastercard","Aspen","West",21.95,1,21.95]
[159,"2010-06-02",46,"Coupon","PayPal","Bellen","West",24.95,1,24.95]
[160,"2010-08-18",41,"No Coupon","Discover","Sunset","West",24.95,3,74.849999999999994]
[161,"2010-04-24",29,"No Coupon","Mastercard","Yanaki","West",19.95,4,79.8]
[162,"2010-12-01",50,"No Coupon","Visa","Yanaki","Mid West",19.95,1,19.95]
[163,"2010-12-31",50,"Coupon","Visa","Carlota","Mid West",22.95,1,22.95]
[164,"2010-04-30",34,"Coupon","PayPal","Carlota","Mid West",22.95,2,45.9]
[165,"2010-03-16",24,"Coupon","American Express","Aspen","West",21.95,3,65.849999999999994]
[166,"2010-01-28",29,"No Coupon","Mastercard","Yanaki","West",19.95,7,139.65]
[167,"2010-08-03",35,"No Coupon","Mastercard","Carlota","Mid West",22.95,1,22.95]
[168,"2010-11-11",24,"No Coupon","Visa","Yanaki","West",19.95,2,39.9]
[169,"2010-12-13",23,"Coupon","Visa","Aspen","South",21.95,5,109.75]
[170,"2010-03-27",31,"No Coupon","PayPal","Carlota","Mid West",22.95,7,160.65]
[171,"2010-10-08",24,"Coupon","PayPal","Bellen","Mid West",24.95,2,49.9]
[172,"2010-08-03",30,"No Coupon","Visa","Carlota","Mid West",22.95,1,22.95]
[173,"2010-03-10",22,"Coupon","Visa","Carlota","West",22.95,2,45.9]
[174,"2010-03-02",43,"No Coupon","Visa","Carlota","East",22.95,3,68.849999999999994]
[175,"2010-01-26",55,"No Coupon","Visa","Carlota","West",22.95,10,229.5]
[176,"2010-05-06",38,"No Coupon","American Express","Delicate Arch","West",29.95,1,29.95]
[177,"2010-03-10",28,"Coupon","Visa","Yanaki","West",19.95,2,39.9]
[178,"2010-11-18",30,"Coupon","PayPal","Aspen","Mid West",21.95,2,43.9]
[179,"2010-01-30",35,"Coupon","Discover","Yanaki","West",19.95,1,19.95]
[180,"2010-07-02",41,"No Coupon","Visa","Delicate Arch","West",29.95,2,59.9]
[181,"2010-10-13",28,"Coupon","Discover","Yanaki","East",19.95,5,99.75]
[182,"2010-02-07",65,"No Coupon","Discover","Bellen","Mid West",24.95,7,174.65]
[183,"2010-06-05",20,"No Coupon","Mastercard","Aspen","West",21.95,3,65.849999999999994]
[184,"2010-11-02",39,"No Coupon","Visa","Sunset","Mid West",24.95,5,124.75]
[185,"2010-12-13",19,"No Coupon","Visa","Aspen","East",21.95,4,87.8]
[186,"2010-10-23",64,"No Coupon","Visa","Carlota","West",22.95,10,229.5]
[187,"2010-12-22",42,"Coupon","PayPal","Yanaki","South",19.95,5,99.75]
[188,"2010-08-21",24,"Coupon","PayPal","Yanaki","Mid West",19.95,1,19.95]
[189,"2010-08-28",24,"Coupon","PayPal","Yanaki","Mid West",19.95,1,19.95]
[190,"2010-06-20",18,"No Coupon","American Express","Bellen","Mid West",24.95,4,99.8]
[191,"2010-04-30",36,"Coupon","Mastercard","Bellen","East",24.95,1,24.95]
[192,"2010-10-14",61,"No Coupon","Mastercard","Carlota","Mid West",22.95,5,114.75]
[193,"2010-08-04",22,"No Coupon","Visa","Yanaki","West",19.95,3,59.849999999999994]
[194,"2010-10-28",55,"Coupon","PayPal","Aspen","West",21.95,2,43.9]
[195,"2010-11-04",27,"No Coupon","American Express","Sunset","West",24.95,3,74.849999999999994]
[196,"2010-01-05",49,"No Coupon","PayPal","Yanaki","Mid West",19.95,1,19.95]
[197,"2010-12-11",29,"Coupon","Visa","Carlota","West",22.95,1,22.95]
[198,"2010-07-18",33,"No Coupon","PayPal","Aspen","West",21.95,7,153.65]
[199,"2010-05-31",52,"No Coupon","Visa","Yanaki","West",19.95,2,39.9]
[200,"2010-12-16",26,"Coupon","PayPal","Aspen","West",21.95,6,131.69999999999999]

{"sheet":"Skew","index":68,"n_rows":44,"n_cols":4,"rows_kept":44,"cut":false,"hidden":false,"merged":[]}
[null,"Skew tells to which way the distribution is tilting. If the average is being pulled up by a few big values, the skew is positive, or to the right. If the average is being pulled down by a few small values, the skew is negative, or to the left. Range of Skew is between -3 and 3."]
[null,"If the Skew is 0, the Mean = Median = Mode = Normal or Bell Distribution"]
[null,"We can use the SKEW function to calculate the Skew"]
[]
[]
[]
[]
[]
[]
[]
[null,"Moderate Skew","No Skew","Highly Skewed"]
[null,"Negative (Left) Skew\nsmall values pull Mean down","No Skew (Normal or Bell)\nMean = Median = Mode","Positive (Right) Skew\nbig values pull Mean up"]
["count = n",{"$f":"COUNT(B21:B30)","v":10},{"$f":"COUNT(C21:C30)","v":10},10]
["Skew",{"$f":"B13/((B13-1)*(B13-2))*SUMPRODUCT(((B21:B30-AVERAGE(B21:B30))/_xlfn.STDEV.S(B21:B30))^3)","v":-0.64052176797398908},{"$f":"C13/((C13-1)*(C13-2))*SUMPRODUCT(((C21:C30-AVERAGE(C21:C30))/_xlfn.STDEV.S(C21:C30))^3)","v":-1.1277285554160596E-2},1.5524906262931217]
["Skew"]
["Mean"]
["Median"]
["Mode"]
[null,"Moderate Skew","No Skew","Highly Skewed"]
[null,"Data 1","Data 2","Data 3"]
[null,7,7.9,1]
[null,43,15,7]
[null,33,11,7]
[null,21,21,12]
[null,15,25,11]
[null,31,25,14]
[null,36,27,2]
[null,43,35,1.9]
[null,48,38,39]
[null,49,41,49]
[]
["Labels","Frequency","Frequency","Frequency"]
[{"$f":"A40&\"-\"&B40-1","v":"0-9"},{"$f":"FREQUENCY(B21:B30,B40:B44)","v":1},{"$f":"FREQUENCY(C21:C30,C40:C44)","v":1},{"$f":"FREQUENCY(D21:D30,D40:D44)","v":5}]
[{"$f":"A41&\"-\"&B41-1","v":"10-19"},1,2,3]
[{"$f":"A42&\"-\"&B42-1","v":"20-29"},1,4,0]
[{"$f":"A43&\"-\"&B43-1","v":"30-39"},3,2,1]
[{"$f":"A44&\"-\"&B44-1","v":"40-49"},4,1,1]
[]
["Low","Bins","Bins","Bins"]
[{"$f":"B40-10","v":0},10,10,10]
[{"$f":"B41-10","v":10},20,20,20]
[{"$f":"B42-10","v":20},30,30,30]
[{"$f":"B43-10","v":30},40,40,40]
[40,50,50,50]

{"sheet":"SkewAN","index":69,"n_rows":44,"n_cols":4,"rows_kept":44,"cut":false,"hidden":false,"merged":[]}
[null,"Skew tells to which way the distribution is tilting. If the average is being pulled up by a few big values, the skew is positive, or to the right. If the average is being pulled down by a few small values, the skew is negative, or to the left. Range of Skew is between -3 and 3."]
[null,"If the Skew is 0, the Mean = Median = Mode = Normal or Bell Distribution"]
[null,"We can use the SKEW function to calculate the Skew"]
[]
[]
[]
[]
[]
[]
[]
[null,"Moderate Skew","No Skew","Highly Skewed"]
[null,"Negative (Left) Skew\nsmall values pull Mean down","No Skew (Normal or Bell)\nMean = Median = Mode","Positive (Right) Skew\nbig values pull Mean up"]
["count = n",{"$f":"COUNT(B21:B30)","v":10},{"$f":"COUNT(C21:C30)","v":10},10]
["Skew",{"$f":"B13/((B13-1)*(B13-2))*SUMPRODUCT(((B21:B30-B16)/_xlfn.STDEV.S(B21:B30))^3)","v":-0.64052176797398908},{"$f":"C13/((C13-1)*(C13-2))*SUMPRODUCT(((C21:C30-C16)/_xlfn.STDEV.S(C21:C30))^3)","v":-1.1277285554160596E-2},1.5524906262931217]
["Skew",{"$f":"SKEW(B21:B30)","v":-0.64052176797398896},{"$f":"SKEW(C21:C30)","v":-1.1277285554160533E-2},{"$f":"SKEW(D21:D30)","v":1.5524906262931217}]
["Mean",{"$f":"AVERAGE(B21:B30)","v":32.6},{"$f":"AVERAGE(C21:C30)","v":24.59},{"$f":"AVERAGE(D21:D30)","v":14.39}]
["Median",{"$f":"MEDIAN(B21:B30)","v":34.5},{"$f":"MEDIAN(C21:C30)","v":25},{"$f":"MEDIAN(D21:D30)","v":9}]
["Mode",{"$f":"MODE(B21:B30)","v":43},{"$f":"MODE(C21:C30)","v":25},{"$f":"MODE(D21:D30)","v":7}]
[null,"Moderate Skew","No Skew","Highly Skewed"]
[null,"Data 1","Data 2","Data 3"]
[null,7,7.9,1]
[null,43,15,7]
[null,33,11,7]
[null,21,21,12]
[null,15,25,11]
[null,31,25,14]
[null,36,27,2]
[null,43,35,1.9]
[null,48,38,39]
[null,49,41,49]
[]
["Labels","Frequency","Frequency","Frequency"]
[{"$f":"A40&\"-\"&B40-1","v":"0-9"},{"$f":"FREQUENCY(B21:B30,B40:B44)","v":1},{"$f":"FREQUENCY(C21:C30,C40:C44)","v":1},{"$f":"FREQUENCY(D21:D30,D40:D44)","v":5}]
[{"$f":"A41&\"-\"&B41-1","v":"10-19"},1,2,3]
[{"$f":"A42&\"-\"&B42-1","v":"20-29"},1,4,0]
[{"$f":"A43&\"-\"&B43-1","v":"30-39"},3,2,1]
[{"$f":"A44&\"-\"&B44-1","v":"40-49"},4,1,1]
[]
["Low","Bins","Bins","Bins"]
[{"$f":"B40-10","v":0},10,10,10]
[{"$f":"B41-10","v":10},20,20,20]
[{"$f":"B42-10","v":20},30,30,30]
[{"$f":"B43-10","v":30},40,40,40]
[40,50,50,50]

{"sheet":"z","index":70,"n_rows":18,"n_cols":5,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
["z = z-score = standardized value"]
["Number of Standard Deviations a particular x is from the mean (Xbar)"]
["Measure of relative location of a particular x in a data set\nParticularly good for comparing values from different data sets!"]
["z > zero, x value > mean"]
["z < zero, x value < mean"]
["z = zero, x value = mean"]
["Who did better? You or your sister?",null,null,"Joe",73]
["Your Calculus Test score =",78,null,"z score",{"$f":"(E7-B9)/B10","v":0}]
["Mean for Calculus Test =",73]
["Standard Deviation for Calculus Test =",3]
["z = (x - Xbar)/s =",null,{"$f":"IF(B11=\"\",\"\",FIXED(B11,2)&\" standard deviations \"&IF(B11>0,\"above\",\"below\")&\" the mean\")","v":""}]
["STANDARDIZE function",null,{"$f":"IF(B12=\"\",\"\",\"relative location of a particular x in a data set\")","v":""}]
["Sister's History Test score =",93]
["Mean for History Test =",96]
["Standard Deviation for History Test =",3]
["z = (x - Xbar)/s =",null,{"$f":"IF(B16=\"\",\"\",FIXED(B16,2)&\" standard deviations \"&IF(B16>0,\"above\",\"below\")&\" the mean\")","v":""}]
["STANDARDIZE function",null,{"$f":"IF(B17=\"\",\"\",\"relative location of a particular x in a data set\")","v":""}]
["When you are calculating a z-score, you are taking the \"Deviation\" and dividing it by SD, which just means that you are determining \"the number of standard deviations\" the value is above or below the mean!!"]

{"sheet":"z (an)","index":71,"n_rows":18,"n_cols":3,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
["z = z-score = standardized value"]
["Number of Standard Deviations a particular x is from the mean (Xbar)"]
["Measure of relative location of a particular x in a data set\nParticularly good for comparing values from different data sets!"]
["z > zero, x value > mean"]
["z < zero, x value < mean"]
["z = zero, x value = mean"]
["Who did better? You or your sister?"]
["Your Calculus Test score =",78]
["Mean for Calculus Test =",73]
["Standard Deviation for Calculus Test =",3]
["z = (x - Xbar)/s =",{"$f":"(B8-B9)/B10","v":1.6666666666666667},{"$f":"IF(B11=\"\",\"\",FIXED(B11,2)&\" standard deviations \"&IF(B11>0,\"above\",\"below\")&\" the mean\")","v":"1.67 standard deviations above the mean"}]
["STANDARDIZE function",{"$f":"STANDARDIZE(B8,B9,B10)","v":1.6666666666666667},{"$f":"IF(B12=\"\",\"\",\"relative location of a particular x in a data set\")","v":"relative location of a particular x in a data set"}]
["Sister's History Test score =",93]
["Mean for History Test =",96]
["Standard Deviation for History Test =",3]
["z = (x - Xbar)/s =",{"$f":"(B13-B14)/B15","v":-1},{"$f":"IF(B16=\"\",\"\",FIXED(B16,2)&\" standard deviations \"&IF(B16>0,\"above\",\"below\")&\" the mean\")","v":"-1.00 standard deviations below the mean"}]
["STANDARDIZE function",{"$f":"STANDARDIZE(B13,B14,B15)","v":-1},{"$f":"IF(B17=\"\",\"\",\"relative location of a particular x in a data set\")","v":"relative location of a particular x in a data set"}]
["When you are calculating a z-score, you are taking the \"Deviation\" and dividing it by SD, which just means that you are determining \"the number of standard deviations\" the value is above or below the mean!!"]

{"sheet":"Chebyshev","index":72,"n_rows":26,"n_cols":11,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
["Russian Mathematician, P.L. Chebyshev (1821-1894)"]
["Chebyshev's Theorem"]
["Allows us to make a statement about the proportion of data values that must be within a specified number of standard deviations of the mean.\nFor example:\n82.6% of the students must have a test score between 58 and 82",null,null,null,null,null,null,null,null,null," =1-1/0.5^2"]
["Rule:\nAt least (1 - 1/z^2) of the values in any data set will be\n within z standard deviations of the mean, where z is\n any value greater than 1.\n",null,null,null,null,null,null,null,null,null,{"$f":"1-1/0.5^2","v":-3}]
["Real power of this Theorem:\nApplies to any data set regardless of the shape of the distribution of the data!",null,null,null,null,null,null,"Proportion of values","Lie between (standard deviations)"]
[{"$f":"\"At least \"&H6&\", or \"&TEXT(H6,\"0.00%\")&\", of the data values must be within z = \"&I6&\" standard deviations of the mean\"","v":"At least 0.75, or 75.00%, of the data values must be within z = 2 standard deviations of the mean"},null,null,null,null,null,null,0.75,2]
[{"$f":"\"At least \"&H7&\", or \"&TEXT(H7,\"0.00%\")&\", of the data values must be within z = \"&I7&\" standard deviations of the mean\"","v":"At least 0.89, or 89.00%, of the data values must be within z = 3 standard deviations of the mean"},null,null,null,null,null,null,0.89,3]
[{"$f":"\"At least \"&H8&\", or \"&TEXT(H8,\"0.00%\")&\", of the data values must be within z = \"&I8&\" standard deviations of the mean\"","v":"At least 0.94, or 94.00%, of the data values must be within z = 4 standard deviations of the mean"},null,null,null,null,null,null,0.94,4]
[]
[null,null,null,"Given the Proportions from Chebyshev's Theorem, what are the low and high values?"]
["Sample Mean","Sample SD",null,"SD","SD","SD"]
["Xbar","s",null,2,3,4]
[75,5]
[]
[null,null,null,{"$f":"IF(OR(D14=\"\"),\"\",\"At least \"&TEXT(INDEX($H$6:$H$8,MATCH(D12,$I$6:$I$8,0)),\"0.00%\")&\" of the values lie between \"&FIXED(D13,1)&\" and \"&FIXED(D14,1)&\" (+/- \"&D12&\" standard deviations.)\")","v":""},{"$f":"IF(OR(E14=\"\"),\"\",\"At least \"&TEXT(INDEX($H$6:$H$8,MATCH(E12,$I$6:$I$8,0)),\"0.00%\")&\" of the values lie between \"&FIXED(E13,1)&\" and \"&FIXED(E14,1)&\" (+/- \"&E12&\" standard deviations.)\")","v":""},{"$f":"IF(OR(F14=\"\"),\"\",\"At least \"&TEXT(INDEX($H$6:$H$8,MATCH(F12,$I$6:$I$8,0)),\"0.00%\")&\" of the values lie between \"&FIXED(F13,1)&\" and \"&FIXED(F14,1)&\" (+/- \"&F12&\" standard deviations.)\")","v":""}]
[]
[null,null,null,"Given two values, we can calculate the proportion of values that should lie between these two values using Chebyshev's Theorem"]
[null,null,null,"Upper & Lower Value","z","Proportion of values between these two",null,null,"or"]
[null,null,null,67,null,null,"1-1/z^2"]
[null,null,null,83]
[null,null,null,{"$f":"IF(F19=\"\",\"\",\"At least \"&TEXT(F19,\"0.00%\")&\" of the scores must be between \"&D19&\" and \"&D20&\".\")","v":""}]
[]
[null,null,null,"According to Chebyshev's Theorem, at least what percent of any data set will be within 1.8 standard deviation of the mean?"]
[null,null,null,null,"z =","Proportion of values between these two"]
[null,null,null,null,1.8,null,"1-1/z^2"]
[null,null,null,{"$f":"IF(F25=\"\",\"\",\"Accoring to Chebyshev's Theorem, at least \"&TEXT(F25,\"0.00%\")&\" of any data set will be within +/- 1.8 standard deviation of the mean.\")","v":""}]

{"sheet":"Chebyshev (an)","index":73,"n_rows":26,"n_cols":11,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
["Russian Mathematician, P.L. Chebyshev (1821-1894)"]
["Chebyshev's Theorem"]
["Allows us to make a statement about the proportion of data values that must be within a specified number of standard deviations of the mean.\nFor example:\n82.6% of the students must have a test score between 58 and 82",null,null,null,null,null,null,null,null,null," =1-1/0.5^2"]
["Rule:\nAt least (1 - 1/z^2) of the values in any data set will be\n within z standard deviations of the mean, where z is\n any value greater than 1.\n",null,null,null,null,null,null,null,null,null,{"$f":"1-1/0.5^2","v":-3}]
["Real power of this Theorem:\nApplies to any data set regardless of the shape of the distribution of the data!",null,null,null,null,null,null,"Proportion of values","Lie between (standard deviations)"]
[{"$f":"\"At least \"&H6&\", or \"&TEXT(H6,\"0.00%\")&\", of the data values must be within z = \"&I6&\" standard deviations of the mean\"","v":"At least 0.75, or 75.00%, of the data values must be within z = 2 standard deviations of the mean"},null,null,null,null,null,null,0.75,2]
[{"$f":"\"At least \"&H7&\", or \"&TEXT(H7,\"0.00%\")&\", of the data values must be within z = \"&I7&\" standard deviations of the mean\"","v":"At least 0.89, or 89.00%, of the data values must be within z = 3 standard deviations of the mean"},null,null,null,null,null,null,0.89,3]
[{"$f":"\"At least \"&H8&\", or \"&TEXT(H8,\"0.00%\")&\", of the data values must be within z = \"&I8&\" standard deviations of the mean\"","v":"At least 0.94, or 94.00%, of the data values must be within z = 4 standard deviations of the mean"},null,null,null,null,null,null,0.94,4]
[]
[null,null,null,"Given the Proportions from Chebyshev's Theorem, what are the low and high values?"]
["Sample Mean","Sample SD",null,"SD","SD","SD"]
["Xbar","s",null,2,3,4]
[75,5,null,{"$f":"A13-B13*D12","v":65},{"$f":"A13-B13*E12","v":60},{"$f":"A13-B13*F12","v":55}]
[null,null,null,{"$f":"A13+B13*D12","v":85},{"$f":"A13+B13*E12","v":90},{"$f":"A13+B13*F12","v":95}]
[null,null,null,{"$f":"IF(OR(D14=\"\"),\"\",\"At least \"&TEXT(INDEX($H$6:$H$8,MATCH(D12,$I$6:$I$8,0)),\"0.00%\")&\" of the values lie between \"&FIXED(D13,1)&\" and \"&FIXED(D14,1)&\" (+/- \"&D12&\" standard deviations.)\")","v":"At least 75.00% of the values lie between 65.0 and 85.0 (+/- 2 standard deviations.)"},{"$f":"IF(OR(E14=\"\"),\"\",\"At least \"&TEXT(INDEX($H$6:$H$8,MATCH(E12,$I$6:$I$8,0)),\"0.00%\")&\" of the values lie between \"&FIXED(E13,1)&\" and \"&FIXED(E14,1)&\" (+/- \"&E12&\" standard deviations.)\")","v":"At least 89.00% of the values lie between 60.0 and 90.0 (+/- 3 standard deviations.)"},{"$f":"IF(OR(F14=\"\"),\"\",\"At least \"&TEXT(INDEX($H$6:$H$8,MATCH(F12,$I$6:$I$8,0)),\"0.00%\")&\" of the values lie between \"&FIXED(F13,1)&\" and \"&FIXED(F14,1)&\" (+/- \"&F12&\" standard deviations.)\")","v":"At least 94.00% of the values lie between 55.0 and 95.0 (+/- 4 standard deviations.)"}]
[]
[null,null,null,"Given two values, we can calculate the proportion of values that should lie between these two values using Chebyshev's Theorem"]
[null,null,null,"Upper & Lower Value","z","Proportion of values between these two",null,null,"or"]
[null,null,null,67,{"$f":"(D19-$A$13)/$B$13","v":-1.6},{"$f":"1-1/E20^2","v":0.609375},"1-1/z^2",null,{"$f":"1-1/E19^2","v":0.609375}]
[null,null,null,83,{"$f":"(D20-$A$13)/$B$13","v":1.6}]
[null,null,null,{"$f":"IF(F19=\"\",\"\",\"At least \"&TEXT(F19,\"0.00%\")&\" of the scores must be between \"&D19&\" and \"&D20&\".\")","v":"At least 60.94% of the scores must be between 67 and 83."}]
[]
[null,null,null,"According to Chebyshev's Theorem, at least what percent of any data set will be within 1.8 standard deviation of the mean?"]
[null,null,null,null,"z =","Proportion of values between these two"]
[null,null,null,null,1.8,{"$f":"1-1/E25^2","v":0.69135802469135799},"1-1/z^2"]
[null,null,null,{"$f":"IF(F25=\"\",\"\",\"Accoring to Chebyshev's Theorem, at least \"&TEXT(F25,\"0.00%\")&\" of any data set will be within +/- 1.8 standard deviation of the mean.\")","v":"Accoring to Chebyshev's Theorem, at least 69.14% of any data set will be within +/- 1.8 standard deviation of the mean."}]

{"sheet":"Empirical Rule","index":74,"n_rows":5,"n_cols":12,"rows_kept":5,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,1,"Approximately 68% of Values"]
[null,null,null,null,null,null,null,null,null,null,2,"Approximately 95% of Values"]
[null,null,null,null,null,null,null,null,null,null,3,"Approximately 99% of Values"]

{"sheet":"Normal Distribution","index":75,"n_rows":87,"n_cols":14,"rows_kept":87,"cut":false,"hidden":false,"merged":[]}
[{"$f":"\"Normal Distribution with Mean = \"&B2&\" Standard Deviation = \"&B3","v":"Normal Distribution with Mean = 1 Standard Deviation = 4.9"},null,null,null,null,null,null,null,null,"Mean = µ =",{"$f":"B2","v":1}]
["Mean = µ =",1,null,null,null,null,null,null,null,"Standard Deviation = s =",{"$f":"B3","v":4.9000000000000004}]
["Standard Deviation = s =",4.9000000000000004]
["Increment for Chart",0.5]
[]
[null,"x","f(x)"]
[1,{"$f":"B8-B$4","v":-19},{"$f":"NORMDIST(B7,B$2,B$3,0)","v":1.9638153130417974E-5}]
[2,-18.5,{"$f":"NORMDIST(B8,B$2,B$3,0)","v":2.9629225616879387E-5}]
[3,-18,{"$f":"NORMDIST(B9,B$2,B$3,0)","v":4.4240287759783487E-5}]
[4,-17.5,6.537227043471398E-5]
[5,-17,9.5597641404895464E-5]
[6,-16.5,1.3834987451687294E-4]
[7,-16,1.9814738490896996E-4]
[8,-15.5,2.8085095422437185E-4]
[9,-15,3.9395030936902856E-4]
[10,-14.5,5.4687109755339005E-4]
[11,-14,7.512880482679862E-4]
[12,-13.5,1.0214237976363977E-3]
[13,-13,1.3743060153531123E-3]
[14,-12.5,1.8299486621790268E-3]
[15,-12,2.4114171656461486E-3]
[16,-11.5,3.1447329664804052E-3]
[17,-11,4.0585713199384537E-3]
[18,-10.5,5.1837085306104458E-3]
[19,-10,6.5521819550823134E-3]
[20,-9.5,8.1961388654904314E-3,null,null,"Empirical (Normal) Rule (True when Distribution is bell shaped)"]
[21,-9,1.0146368937583104E-2,null,null,"68% of the values lie between these two values:",null,null,null,null,{"$f":"$B$2-M27*$B$3","v":-3.9000000000000004},{"$f":"$B$2+M27*$B$3","v":5.9},1,"SD"]
[22,-8.5,1.2430539419692261E-2,null,null,"95% of the values lie between these two values:",null,null,null,null,{"$f":"$B$2-M28*$B$3","v":-8.8000000000000007},{"$f":"$B$2+M28*$B$3","v":10.8},2,"SD"]
[23,-8,1.5071180934117035E-2,null,null,"99% (almost all) of the values lie between these two values:",null,null,null,null,{"$f":"$B$2-M29*$B$3","v":-13.700000000000001},{"$f":"$B$2+M29*$B$3","v":15.700000000000001},3,"SD"]
[24,-7.5,1.8083503543544228E-2]
[25,-7,2.1473154595700004E-2]
[26,-6.5,2.5234058720584297E-2]
[27,-6,2.9346502601809852E-2]
[28,-5.5,3.3775639171011264E-2]
[29,-5,3.847058450771737E-2]
[30,-4.5,4.3364263695918073E-2]
[31,-4,4.8374128265281806E-2]
[32,-3.5,5.3403818382455719E-2]
[33,-3,5.8345780259442752E-2]
[34,-2.5,6.3084777718176818E-2]
[35,-2,6.7502162413598021E-2]
[36,-1.5,7.1480696784170628E-2]
[37,-1,7.4909664563390502E-2]
[38,-0.5,7.7689962305902777E-2]
[39,0,7.9738847152492395E-2]
[40,0.5,8.0994024193546899E-2]
[41,{"$f":"B2","v":1},8.141679191865972E-2]
[42,{"$f":"B47+B$4","v":1.5},8.0994024193546899E-2]
[43,2,7.9738847152492395E-2]
[44,2.5,7.7689962305902777E-2]
[45,3,7.4909664563390502E-2]
[46,3.5,7.1480696784170628E-2]
[47,4,6.7502162413598021E-2]
[48,4.5,6.3084777718176818E-2]
[49,5,5.8345780259442752E-2]
[50,5.5,5.3403818382455719E-2]
[51,6,4.8374128265281806E-2]
[52,6.5,4.3364263695918073E-2]
[53,7,3.847058450771737E-2]
[54,7.5,3.3775639171011264E-2]
[55,8,2.9346502601809852E-2]
[56,8.5,2.5234058720584297E-2]
[57,9,2.1473154595700004E-2]
[58,9.5,1.8083503543544228E-2]
[59,10,1.5071180934117035E-2]
[60,10.5,1.2430539419692261E-2]
[61,11,1.0146368937583104E-2]
[62,11.5,8.1961388654904314E-3]
[63,12,6.5521819550823134E-3]
[64,12.5,5.1837085306104458E-3]
[65,13,4.0585713199384537E-3]
[66,13.5,3.1447329664804052E-3]
[67,14,{"$f":"NORMDIST(B73,B$2,B$3,0)","v":2.4114171656461486E-3}]
[68,14.5,1.8299486621790268E-3]
[69,15,1.3743060153531123E-3]
[70,15.5,1.0214237976363977E-3]
[71,16,7.512880482679862E-4]
[72,16.5,5.4687109755339005E-4]
[73,17,3.9395030936902856E-4]
[74,17.5,2.8085095422437185E-4]
[75,18,1.9814738490896996E-4]
[76,18.5,1.3834987451687294E-4]
[77,19,9.5597641404895464E-5]
[78,19.5,6.537227043471398E-5]
[79,20,4.4240287759783487E-5]
[80,20.5,2.9629225616879387E-5]
[81,21,1.9638153130417974E-5]

{"sheet":"Bell(1)","index":76,"n_rows":28,"n_cols":4,"rows_kept":28,"cut":false,"hidden":false,"merged":[]}
["Approximately 68% of Values lie between 1 SD above or below the mean."]
["Approximately 95% of Values lie between 2 SD above or below the mean."]
["Approximately 99% of Values lie between 3 SD above or below the mean."]
[]
[]
[]
[]
[]
[]
["Distribution had a bell (Normal) shape"]
["Pop. Stats Test Mean",83,"Mew"]
["Pop. Standard Deviation",5,"Sigma"]
[]
["68% of the scores will lie between what two values?"]
["Lower",null,null,0.68]
["Upper"]
[{"$f":"IF(B16=\"\",\"\",\"Aproximately \"&TEXT(D15,\"0.00%\")&\" lie between \"&B15&\" and \"&B16&\".\")","v":""}]
[]
["95% of the scores will lie between what two values?"]
["Lower",null,null,0.95]
["Upper"]
[{"$f":"IF(B21=\"\",\"\",\"Aproximately \"&TEXT(D20,\"0.00%\")&\" lie between \"&B20&\" and \"&B21&\".\")","v":""}]
[]
["What percent of the values lie below a score of 83?",null,null,0.5]
[{"$f":"IF(D24=\"\",\"\",\"Aproximately \"&TEXT(D24,\"0.00%\")&\" lie below \"&$B$11)","v":"Aproximately 50.00% lie below 83"}]
[]
["What percent of the values lie above a score of 83?",null,null,0.5]
[{"$f":"IF(D27=\"\",\"\",\"Aproximately \"&TEXT(D27,\"0.00%\")&\" lie above \"&$B$11)","v":"Aproximately 50.00% lie above 83"}]

{"sheet":"Bell(1an)","index":77,"n_rows":28,"n_cols":4,"rows_kept":28,"cut":false,"hidden":false,"merged":[]}
["Approximately 68% of Values lie between 1 SD above or below the mean."]
["Approximately 95% of Values lie between 2 SD above or below the mean."]
["Approximately 99% of Values lie between 3 SD above or below the mean."]
[]
[]
[]
[]
[]
[]
["Distribution had a bell (Normal) shape"]
["Pop. Stats Test Mean",83,"Mu"]
["Pop. Standard Deviation",5,"Sigma"]
[]
["68% of the scores will lie between what two values?"]
["Lower",{"$f":"B11-B12","v":78},null,0.68]
["Upper",{"$f":"B11+B12","v":88}]
[{"$f":"IF(B16=\"\",\"\",\"Aproximately \"&TEXT(D15,\"0.00%\")&\" lie between \"&B15&\" and \"&B16&\".\")","v":"Aproximately 68.00% lie between 78 and 88."}]
[]
["95% of the scores will lie between what two values?"]
["Lower",{"$f":"B11-B12*2","v":73},null,0.95]
["Upper",{"$f":"B11+B12*2","v":93}]
[{"$f":"IF(B21=\"\",\"\",\"Aproximately \"&TEXT(D20,\"0.00%\")&\" lie between \"&B20&\" and \"&B21&\".\")","v":"Aproximately 95.00% lie between 73 and 93."}]
[]
["What percent of the values lie below a score of 83?",null,null,0.5]
[{"$f":"IF(D24=\"\",\"\",\"Aproximately \"&TEXT(D24,\"0.00%\")&\" lie below \"&$B$11)","v":"Aproximately 50.00% lie below 83"}]
[]
["What percent of the values lie above a score of 83?",null,null,0.5]
[{"$f":"IF(D27=\"\",\"\",\"Aproximately \"&TEXT(D27,\"0.00%\")&\" lie above \"&$B$11)","v":"Aproximately 50.00% lie above 83"}]

{"sheet":"Bell(2)","index":78,"n_rows":17,"n_cols":6,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
[" +/- 1 SD","Approximately 68% of Values"]
[" +/- 2 SD","Approximately 95% of Values"]
[" +/- 3 SD","Approximately 99% of Values"]
[]
["Retail price per gallon distribution is bell shaped"]
["Mean regular gas per gallon",null,null,2.6]
["Standard Deviation =",null,null,0.15]
[]
["lower",{"$f":"A9&\" z (#SD)\"","v":"lower z (#SD)"},"upper",{"$f":"C9&\" z (#SD)\"","v":"upper z (#SD)"},"meaning","Total %"]
[2.4500000000000002,null,2.75,null,{"$f":"IF(F10=\"\",\"\",\"Aproximately \"&TEXT(F10,\"0.00%\")&\" of values lie between \"&DOLLAR(A10)&\" and \"&DOLLAR(C10,2))","v":""}]
[2.2999999999999998,null,2.75,null,{"$f":"IF(F11=\"\",\"\",\"Aproximately \"&TEXT(F11,\"0.00%\")&\" of values lie between \"&DOLLAR(A11)&\" and \"&DOLLAR(C11,2))","v":""}]
[null,null,2.75,null,{"$f":"IF(F12=\"\",\"\",\"Aproximately \"&TEXT(F12,\"0.00%\")&\" of values are above \"&C12)","v":""}]
[]
[null,"SD","%","1/2 area"]
[null,{"$f":"A1","v":" +/- 1 SD"},0.68]
[null,{"$f":"A2","v":" +/- 2 SD"},0.95]
[null,{"$f":"A3","v":" +/- 3 SD"},0.99]

{"sheet":"Bell(2an)","index":79,"n_rows":17,"n_cols":6,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
[" +/- 1 SD","Approximately 68% of Values"]
[" +/- 2 SD","Approximately 95% of Values"]
[" +/- 3 SD","Approximately 99% of Values"]
[]
["Retail price per gallon distribution is bell shaped"]
["Mean regular gas per gallon",null,null,2.6]
["Standard Deviation =",null,null,0.15]
[]
["lower",{"$f":"A9&\" z (#SD)\"","v":"lower z (#SD)"},"upper",{"$f":"C9&\" z (#SD)\"","v":"upper z (#SD)"},"meaning","Total %"]
[2.4500000000000002,{"$f":"(A10-$D$6)/$D$7","v":-0.99999999999999944},2.75,{"$f":"(C10-$D$6)/$D$7","v":0.99999999999999944},{"$f":"IF(F10=\"\",\"\",\"Aproximately \"&TEXT(F10,\"0.00%\")&\" of values lie between \"&DOLLAR(A10)&\" and \"&DOLLAR(C10,2))","v":"Aproximately 68.00% of values lie between $2.45 and $2.75"},0.68]
[2.2999999999999998,{"$f":"(A11-$D$6)/$D$7","v":-2.0000000000000018},2.75,{"$f":"(C11-$D$6)/$D$7","v":0.99999999999999944},{"$f":"IF(F11=\"\",\"\",\"Aproximately \"&TEXT(F11,\"0.00%\")&\" of values lie between \"&DOLLAR(A11)&\" and \"&DOLLAR(C11,2))","v":"Aproximately 81.50% of values lie between $2.30 and $2.75"},{"$f":"D15+D16","v":0.81499999999999995}]
[null,null,2.75,{"$f":"(C12-$D$6)/$D$7","v":0.99999999999999944},{"$f":"IF(F12=\"\",\"\",\"Aproximately \"&TEXT(F12,\"0.00%\")&\" of values are above \"&C12)","v":"Aproximately 16.00% of values are above 2.75"},{"$f":"0.5-D15","v":0.15999999999999998}]
[]
[null,"SD","%","1/2 area"]
[null,{"$f":"A1","v":" +/- 1 SD"},0.68,{"$f":"C15/2","v":0.34}]
[null,{"$f":"A2","v":" +/- 2 SD"},0.95,{"$f":"C16/2","v":0.47499999999999998}]
[null,{"$f":"A3","v":" +/- 3 SD"},0.99,{"$f":"C17/2","v":0.495}]

{"sheet":"Bell&Cheb","index":80,"n_rows":19,"n_cols":7,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["If the distribution of weights for a Lettuce Filling Machine are normally distributed (Bell Shape) with a mean of 13 oz and a standard deviation of .1 oz, what percent of the values should lie between 2 standard deviations and what are the low and high values associated with the percentage?"]
[]
["Mean",13,"oz"]
["SD",0.1,"oz"]
["# SD",2]
["Percent =",0.95,null,"Empirical Rule"]
["Lower Values"]
["Upper Value"]
[{"$f":"IF(B8=\"\",\"\",\"Because the distribution is bell shaped, we can say that approximately \"&TEXT(B6,\"0.00%\")&\" of the values should lie between \"&B8&\" oz. and \"&B7&\" oz.\")","v":""}]
[]
["Mean",13,"oz"]
["SD",0.1,"oz"]
["# SD",2]
["Percent =",0.75,null,"Chebyshev's Theorem",null,null,{"$f":"1-1/B13^2","v":0.75}]
["Lower Values"]
["Upper Value"]
[{"$f":"IF(B16=\"\",\"\",\"Because the distribution is not bell shaped, we can say that approximately \"&TEXT(B14,\"0.00%\")&\" of the values should lie between \"&B16&\" oz. and \"&B15&\" oz.\")","v":""}]
[]
["."]

{"sheet":"Bell&ChebAN","index":81,"n_rows":19,"n_cols":4,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["If the distribution of weights for a Lettuce Filling Machine are normally distributed (Bell Shape) with a mean of 13 oz and a standard deviation of .1 oz, what percent of the values should lie between 2 standard deviations and what are the low and high values associated with the percentage?"]
[]
["Mean",13,"oz"]
["SD",0.1,"oz"]
["# SD",2]
["Percent =",0.95,null,"Empirical Rule"]
["Lower Values",{"$f":"B3-B4*B5","v":12.8}]
["Upper Value",{"$f":"B3+B4*B5","v":13.2}]
[{"$f":"IF(B8=\"\",\"\",\"Because the distribution is bell shaped, we can say that approximately \"&TEXT(B6,\"0.00%\")&\" of the values should lie between \"&B8&\" oz. and \"&B7&\" oz.\")","v":"Because the distribution is bell shaped, we can say that approximately 95.00% of the values should lie between 13.2 oz. and 12.8 oz."}]
[]
["Mean",13,"oz"]
["SD",0.1,"oz"]
["# SD",2]
["Percent =",0.75,null,"Chebyshev's Theorem"]
["Lower Values",{"$f":"$B$11-$B$12*$B$13","v":12.8}]
["Upper Value",{"$f":"$B$11+$B$12*$B$13","v":13.2}]
[{"$f":"IF(B16=\"\",\"\",\"Because the distribution is not bell shaped, we can say that approximately \"&TEXT(B14,\"0.00%\")&\" of the values should lie between \"&B16&\" oz. and \"&B15&\" oz.\")","v":"Because the distribution is not bell shaped, we can say that approximately 75.00% of the values should lie between 13.2 oz. and 12.8 oz."}]
[]
["."]

{"sheet":"Outlier","index":82,"n_rows":32,"n_cols":12,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["Detecting Outliers"]
["An outlier is an unusually small or unusually large value in a data set."]
["A data value with a z-score less than -3 or greater than +3 might be considered an outlier."]
["   It might be:\n1)an incorrectly recorded data value\n2)a data value that was incorrectly included in the data set\n3) a correctly recorded data value that belongs in\n     the data set"]
["ABS is absolute Value function in Excel (Distance away from zero)"]
[]
["Mean",50]
["SD",15]
["Count",{"$f":"COUNT(B22:B32)","v":11}]
["Excel"]
["Quartile 1",{"$f":"QUARTILE($B$22:$B$32,C11)","v":47.5},1]
["Quartile 3",{"$f":"QUARTILE($B$22:$B$32,C12)","v":60.5},3]
["by hand: Roundup if decimal, take ave. of i and i + 1 if whole #"]
[null,"Value","i"]
["Quartile 1",{"$f":"B24","v":45},{"$f":"D15*$B$9","v":2.75},0.25]
["Quartile 3",{"$f":"B30","v":62},{"$f":"D16*$B$9","v":8.25},0.75]
["Interquartile Range",{"$f":"B16-B15","v":17}]
["Lower Limit for Outlier",{"$f":"B15-B17*1.5","v":19.5},"Q1 - 1.5*(Q3-Q1) or 0"]
["Upper Limit for Outlier",{"$f":"B16+1.5*B17","v":87.5},"Q3 + 1.5*(Q3-Q1)"]
[]
["No","Sales",null,"z","Outlier = z >3",null,null,null,null,null,"Outlier Limit = Q1 - 1.5*Interquartile range","Outlier Limit = Q3 + 1.5*Interquartile range"]
[1,42]
[2,43]
[3,45]
[4,50]
[5,51]
[6,51]
[7,53]
[8,59]
[9,62]
[10,92]
[11,500]

{"sheet":"Outlier (an)","index":83,"n_rows":32,"n_cols":12,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["Detecting Outliers"]
["An outlier is an unusually small or unusually large value in a data set."]
["A data value with a z-score less than -3 or greater than +3 might be considered an outlier."]
["   It might be:\n1)an incorrectly recorded data value\n2)a data value that was incorrectly included in the data set\n3) a correctly recorded data value that belongs in\n     the data set"]
["ABS is absolute Value function in Excel (Distance away from zero)"]
[]
["Mean",50]
["SD",15]
["Count",{"$f":"COUNT(B22:B32)","v":11}]
["Excel"]
["Quartile 1",{"$f":"QUARTILE($B$22:$B$32,C11)","v":47.5},1]
["Quartile 3",{"$f":"QUARTILE($B$22:$B$32,C12)","v":60.5},3]
["by hand: Roundup if decimal, take ave. of i and i + 1 if whole #"]
[null,"Value","i"]
["Quartile 1",{"$f":"B24","v":45},{"$f":"D15*$B$9","v":2.75},0.25]
["Quartile 3",{"$f":"B30","v":62},{"$f":"D16*$B$9","v":8.25},0.75]
["Interquartile Range",{"$f":"B16-B15","v":17}]
["Lower Limit for Outlier",{"$f":"B15-B17*1.5","v":19.5},"Q1 - 1.5*(Q3-Q1) or 0"]
["Upper Limit for Outlier",{"$f":"B16+1.5*B17","v":87.5},"Q3 + 1.5*(Q3-Q1)"]
[]
["No","Sales",null,"z","Outlier = z >3",null,null,null,null,null,"Outlier Limit = Q1 - 1.5*Interquartile range","Outlier Limit = Q3 + 1.5*Interquartile range"]
[1,42,null,{"$f":"(B22-$B$7)/$B$8","v":-0.53333333333333333},{"$f":"ABS(D22)>3","v":false},null,null,null,null,null,{"$f":"B22<$B$18","v":false},{"$f":"B22>$B$19","v":false}]
[2,43,null,-0.46666666666666667,{"$f":"ABS(D23)>3","v":false},null,null,null,null,null,false,false]
[3,45,null,-0.33333333333333331,false,null,null,null,null,null,false,false]
[4,50,null,0,false,null,null,null,null,null,false,false]
[5,51,null,6.6666666666666666E-2,false,null,null,null,null,null,false,false]
[6,51,null,6.6666666666666666E-2,false,null,null,null,null,null,false,false]
[7,53,null,0.2,false,null,null,null,null,null,false,false]
[8,59,null,0.6,false,null,null,null,null,null,false,false]
[9,62,null,0.8,false,null,null,null,null,null,false,false]
[10,92,null,2.8,false,null,null,null,null,null,false,true]
[11,500,null,30,true,null,null,null,null,null,false,true]