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[{"$f":"\"The sample data strongly indicate that Accounting Majors (AM) make more than Marketing Majors (MM) when they graduate. The average salary difference between AM and MM is \"&E20&\" - \"&K20&\" = \"&ROUND(ABS(E20-K20),2)&\". In addition 25% of the AM make \"&DOLLAR(K24*1000)&\" or more; whereas for MM, 25% of the MM make \"&DOLLAR(E28*1000)&\" or more.\"","v":"The sample data strongly indicate that Accounting Majors (AM) make more than Marketing Majors (MM) when they graduate. The average salary difference between AM and MM is 36.3 - 45.7 = 9.4. In addition 25% of the AM make $49,750.00 or more; whereas for MM, 25% of the MM make $39,500.00 or more."}]

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[null,null,null,null,0.9,{"$f":"\"Excel Percentile \"&TEXT(E30,\"0.00%\")","v":"Excel Percentile 90.00%"},{"$f":"_xlfn.PERCENTILE.INC(Cost,E30)","v":237.00000000000003},{"$f":"_xlfn.PERCENTILE.EXC(Cost,E30)","v":253.00000000000006}]
[null,null,null,null,0.25,{"$f":"\"Excel Percentile \"&TEXT(E31,\"0.00%\")","v":"Excel Percentile 25.00%"},{"$f":"_xlfn.PERCENTILE.INC(Cost,E31)","v":115},{"$f":"_xlfn.PERCENTILE.EXC(Cost,E31)","v":115}]
[null,null,null,null,0.75,{"$f":"\"Excel Percentile \"&TEXT(E32,\"0.00%\")","v":"Excel Percentile 75.00%"},{"$f":"_xlfn.PERCENTILE.INC(Cost,E32)","v":183.75},{"$f":"_xlfn.PERCENTILE.EXC(Cost,E32)","v":191.25}]
[null,null,0.9,{"$f":"G$24*C33","v":18},{"$f":"\"i = \"&G$24*C33","v":"i = 18"},{"$f":"\"By Hand Percentile \"&TEXT(C33,\"0.00%\")","v":"By Hand Percentile 90.00%"},{"$f":"AVERAGE(G19:G20)","v":245},{"$f":"TEXT(C33,\"0.00%\")&\" of the values are less than or equal to a cost of \"&DOLLAR(G38)&\" and \"&TEXT(1-C33,\"0.00%\")&\" of the values are greater than or equal to a cost of \"&DOLLAR(G38)&\".\"","v":"90.00% of the values are less than or equal to a cost of $245.00 and 10.00% of the values are greater than or equal to a cost of $245.00."}]
[null,null,0.25,{"$f":"G$24*C34","v":5},{"$f":"\"i = \"&G$24*C34","v":"i = 5"},{"$f":"\"By Hand Percentile \"&TEXT(C34,\"0.00%\")","v":"By Hand Percentile 25.00%"},{"$f":"AVERAGE(G6:G7)","v":115}]
[null,null,0.75,{"$f":"G$24*C35","v":15},{"$f":"\"i = \"&G$24*C35","v":"i = 15"},{"$f":"\"By Hand Percentile \"&TEXT(C35,\"0.00%\")","v":"By Hand Percentile 75.00%"},{"$f":"AVERAGE(G16:G17)","v":187.5}]
[]
[null,null,null,null,null,null,"check"]
[null,null,null,null,null,null,{"$f":"IF(D33=INT(D33),AVERAGE(VLOOKUP(D33,VCost,2),VLOOKUP(1+D33,VCost,2)),VLOOKUP(ROUNDUP(D33,0),VCost,2))","v":245}]
[null,null,null,null,null,null,{"$f":"IF(D34=INT(D34),AVERAGE(VLOOKUP(D34,VCost,2),VLOOKUP(1+D34,VCost,2)),VLOOKUP(ROUNDUP(D34,0),VCost,2))","v":115}]
[null,null,null,null,null,null,{"$f":"IF(D35=INT(D35),AVERAGE(VLOOKUP(D35,VCost,2),VLOOKUP(1+D35,VCost,2)),VLOOKUP(ROUNDUP(D35,0),VCost,2))","v":187.5}]

{"sheet":"(9)","index":3,"n_rows":16,"n_cols":8,"rows_kept":16,"cut":false,"hidden":true,"merged":[[11,3,15,5]]}
["No.","Min per month",null,"Count = n = Sample Size",{"$f":"COUNT(Min_per_month)","v":15}]
[1,105,null,"Mean",{"$f":"AVERAGE(Min_per_month)","v":422}]
[2,135,null,"Median",{"$f":"MEDIAN(Min_per_month)","v":380}]
[3,180,null,"Decimal for Percentile",0.85]
[4,210,null,{"$f":"\"i \"&TEXT(E4,\"0.00%\")&\" =\"","v":"i 85.00% ="},{"$f":"E1*E4","v":12.75},null,"check"]
[5,245,null,{"$f":"\"By hand Percentile \"&TEXT(E4,\"0.00%\")&\" =\"","v":"By hand Percentile 85.00% ="},{"$f":"B14","v":690},null,{"$f":"IF(E5=INT(E5),AVERAGE(VLOOKUP(E5,A2:B16,2),VLOOKUP(E5+1,A2:B16,2)),VLOOKUP(ROUNDUP(E5,0),A2:B16,2))","v":690}]
[6,250,null,{"$f":"\"Excel Percentile \"&TEXT(E4,\"0.00%\")&\" =\"","v":"Excel Percentile 85.00% ="},{"$f":"PERCENTILE(Min_per_month,E4)","v":682.5},null,null,"PERCENTRANK function"]
[7,265,null,"Ave Minutes for a plan",750,null,null,{"$f":"PERCENTRANK(Min_per_month,E8)","v":0.88700000000000001}]
[8,380,null,"Decimal for Percentile",0.88775510204081631]
[9,395,null,{"$f":"\"Excel Percentile \"&TEXT(E9,\"0.0000%\")&\" =\"","v":"Excel Percentile 88.7755% ="},{"$f":"PERCENTILE(Min_per_month,E9)","v":750}]
[10,420]
[11,430,null,{"$f":"\"The data suggests that most cell phone users do not use the full amount of time allotted to them. In fact, it is not until the \"&TEXT(E9,\"0.0000%\")&\" percentile that users go over the \"&E8&\" limit. According to the data, \"&TEXT(1-E9,\"0.0000%\")&\" of the users use \"&E8&\" or more minutes per month.\"","v":"The data suggests that most cell phone users do not use the full amount of time allotted to them. In fact, it is not until the 88.7755% percentile that users go over the 750 limit. According to the data, 11.2245% of the users use 750 or more minutes per month."}]
[12,615]
[13,690]
[14,830]
[15,1180]

{"sheet":"(11)","index":4,"n_rows":9,"n_cols":14,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["City",16.2,16.7,15.9,14.4,13.2,15.3,16.8,16,16.100000000000001,15.3,15.2,15.3,16.2]
["Highway",19.399999999999999,20.6,18.3,18.600000000000001,19.2,17.399999999999999,17.2,18.600000000000001,19,21.1,19.399999999999999,18.5,18.7]
[]
["City",null,null,"Highway",null,null,"Difference"]
["Mean",{"$f":"AVERAGE(City)","v":15.584615384615384},null,"Mean",{"$f":"AVERAGE(Highway)","v":18.92307692307692},null,{"$f":"E5-B5","v":3.3384615384615355}]
["Median",{"$f":"MEDIAN(City)","v":15.9},null,"Median",{"$f":"MEDIAN(Highway)","v":18.7},null,{"$f":"E6-B6","v":2.7999999999999989}]
["mode",{"$f":"_xlfn.MODE.SNGL(City)","v":15.3},null,"mode",{"$f":"_xlfn.MODE.SNGL(Highway)","v":19.399999999999999},null,{"$f":"E7-B7","v":4.0999999999999979}]
[]
["With all three different ways to measure what a typical value is, the Highway MPG is higher."]

{"sheet":"(15)","index":5,"n_rows":30,"n_cols":15,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["Sample Data",null,"MIN",{"$f":"MIN(A2:A9)","v":15},null,null,null,null,null,null,null,null,null,{"$f":"A1","v":"Sample Data"},"Y"]
[34,null,"MAX",{"$f":"MAX(A2:A9)","v":34},null,null,null,"If i is decimal, roundup to next integer",null,null,null,null,null,34,1]
[30,null,"Range = Max - Min =",{"$f":"D2-D1","v":19},null,null,null,"If i is whole number, average 1 and 1 + 1",null,null,null,null,null,30,1]
[28,null,null,null,null,null,null,"By Hand Method",null,null,null,null,null,28,1]
[27,null,null,"Excel Method",null,null,null,"Count = n = sample size",{"$f":"COUNT(A2:A9)","v":8},null,"Value",null,null,27,1]
[25,null,{"$f":"\"QUARTILE\"&F6","v":"QUARTILE1"},{"$f":"_xlfn.QUARTILE.INC($A$2:$A$9,F6)","v":23.75},{"$f":"_xlfn.QUARTILE.EXC(A2:$A$9,F6)","v":21.25},1,null,0.25,{"$f":"\"i = index @ \"&H6&\" =\"","v":"i = index @ 0.25 ="},{"$f":"$I$5*H6","v":2},{"$f":"AVERAGE(A7:A8)","v":22.5},null,null,25,1]
[25,null,{"$f":"\"QUARTILE\"&F7","v":"QUARTILE3"},{"$f":"_xlfn.QUARTILE.INC($A$2:$A$9,F7)","v":28.5},{"$f":"_xlfn.QUARTILE.EXC(A3:$A$9,F7)","v":28},3,null,0.75,{"$f":"\"i = index @ \"&H7&\" =\"","v":"i = index @ 0.75 ="},{"$f":"$I$5*H7","v":6},{"$f":"AVERAGE(A3:A4)","v":29},null,null,25,1]
[20,null,"InterQuartile Range = Range for Middle 50% Values =",{"$f":"D7-D6","v":4.75},null,null,null,"InterQuartile Range = Range for Middle 50% Values =",null,null,{"$f":"K7-K6","v":6.5},null,null,20,1]
[15,null,"* small data set makes these value very different than \"by hand\" method",null,null,null,null,null,null,null,null,null,null,15,1]
[]
[null,null,null,"Excel Method",null,null,null,null,null,null,null,null,"Mean",{"$f":"D15","v":25.5},0.5]
[null,null,"Sample Variance = VAR =",{"$f":"_xlfn.VAR.S(A2:A9)","v":34.571428571428569},"squared units"]
[null,null,"Sample Standard Deviation = STDEV =",{"$f":"_xlfn.STDEV.S(A2:A9)","v":5.8797473220733361},{"$f":"\"Not \"&E12","v":"Not squared units"}]
[null,null,"Count",{"$f":"COUNT(A2:A9)","v":8}]
[null,null,"Mean",{"$f":"AVERAGE(A2:A9)","v":25.5}]
[]
[null,"By Hand Method"]
[null,"X","(X - Xbar) (Deviations)","(X - Xbar)^2"]
[null,{"$f":"A2","v":34},{"$f":"B19-$D$15","v":8.5},{"$f":"C19^2","v":72.25}]
[null,30,4.5,20.25]
[null,28,2.5,6.25]
[null,27,1.5,2.25]
[null,25,-0.5,0.25]
[null,25,-0.5,0.25]
[null,20,-5.5,30.25]
[null,15,-10.5,110.25]
[null,null,{"$f":"\"Total must = Zero =\"&SUM(C19:C26)","v":"Total must = Zero =0"},{"$f":"SUM(D19:D26)","v":242}]
[null,null,"Sample Variance",{"$f":"D27/(D14-1)","v":34.571428571428569}]
[null,null,"Sample Standard Deviation",{"$f":"D28^(1/2)","v":5.8797473220733361}]
[null,null,"Sample Standard Deviation",{"$f":"SQRT(D28)","v":5.8797473220733361}]

{"sheet":"(16)","index":6,"n_rows":34,"n_cols":9,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["Scores",null,null,null,null,null,null,"Scores (Data Analysis Add-in Descriptive Statistics)"]
[190,null,"MAX",{"$f":"MAX(A2:A7)","v":190}]
[184,null,"MIN",{"$f":"MIN(A2:A7)","v":168},null,null,null,"Mean",178]
[182,null,"Range",{"$f":"D2-D3","v":22},null,null,null,"Standard Error",3.5402448126271349]
[174,null,"COUNT",{"$f":"COUNT(A2:A7)","v":6},"n = sample size",null,null,"Median",178]
[170,null,"AVERAGE",{"$f":"AVERAGE(A2:A7)","v":178},"Mean",null,null,"Mode",{"$error":"#N/A"}]
[168,null,"VAR",{"$f":"_xlfn.VAR.S(A2:A7)","v":75.2},"Sample Variance","squared units",null,"Standard Deviation",8.6717933554715199]
[null,null,"STDEV",{"$f":"_xlfn.STDEV.S(A2:A7)","v":8.6717933554715199},"Sample Standard Deviation",{"$f":"\"Not \"&F7","v":"Not squared units"},null,"Sample Variance",75.2]
[null,null,"Coefficient of Variation",{"$f":"D8/D6","v":4.8717940199278199E-2},"Great for comparing this SD to others with 1) different means (means for apart), 2) Different SD (SD far apart), 3) SD with different units.","Calculation does not involve multiplying by 100, like in textbook. This is a decimal formatted as a percent.",null,"Kurtosis",-1.7145767315527394]
[null,null,null,null,null,null,null,"Skewness",0.19873677619771249]
[null,null,null,null,null,null,null,"Range",22]
["By Hand Method",null,null,null,null,null,null,"Minimum",168]
["X","(X - Xbar) (Deviations)","(X - Xbar) (Deviations)^2",null,null,null,null,"Maximum",190]
[{"$f":"A2","v":190},{"$f":"A14-D$6","v":12},{"$f":"B14^2","v":144},null,null,null,null,"Sum",1068]
[184,6,36,null,null,null,null,"Count",6]
[182,4,16]
[174,-4,16]
[170,-8,64]
[168,-10,100]
["Totals",{"$f":"SUM(B14:B19)","v":0},{"$f":"SUM(C14:C19)","v":376}]
[null,"Sample Variance",{"$f":"C20/(D5-1)","v":75.2}]
[null,"Sample Standard Deviation",{"$f":"C21^(1/2)","v":8.6717933554715199},{"$f":"SQRT(C21)","v":8.6717933554715199}]
[]
[]
[null,{"$f":"A13","v":"X"},"Y"]
[null,190,1]
[null,184,1]
[null,182,1]
[null,174,1]
[null,170,1]
[null,168,1]
[]
[]
["Mean",{"$f":"D6","v":178},0.5]

{"sheet":"(17)","index":7,"n_rows":18,"n_cols":6,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
[null,null,"Model w DVD",null,"Model without DVD"]
[null,null,450,null,300]
[null,null,300,null,300]
[null,null,400,null,360]
[null,null,500,null,290]
[null,null,400,null,300]
["a","AVERAGE (Mean)",{"$f":"AVERAGE(C2:C6)","v":410},"AVERAGE (Mean)",{"$f":"AVERAGE(E2:E6)","v":310}]
[null,{"$f":"\"From our sample data the average premium paid to get a model with a DVD was \"&DOLLAR(C7-E7)","v":"From our sample data the average premium paid to get a model with a DVD was $100.00"}]
["b","Max",{"$f":"MAX(C2:C6)","v":500},"Max",{"$f":"MAX(E2:E6)","v":360}]
[null,"Min",{"$f":"MIN(C2:C6)","v":300},"Min",{"$f":"MIN(E2:E6)","v":290}]
[null,"Range",null,{"$f":"B11","v":"Range"}]
[null,"Sample Variance",{"$f":"_xlfn.VAR.S(C2:C6)","v":5500},{"$f":"B12","v":"Sample Variance"},{"$f":"_xlfn.VAR.S(E2:E6)","v":800},"squared units"]
[null,"Sample Standard Deviation",{"$f":"_xlfn.STDEV.S(C2:C6)","v":74.16198487095663},{"$f":"B13","v":"Sample Standard Deviation"},{"$f":"_xlfn.STDEV.S(E2:E6)","v":28.284271247461902},{"$f":"\"Not \"&F12","v":"Not squared units"}]
[null,"Coefficient of Variation",{"$f":"C13/C7","v":0.18088288992916252},"Coefficient of Variation",{"$f":"E13/E7","v":9.1239584669231946E-2},"Calculation does not involve multiplying by 100, like in textbook. This is a decimal formatted as a percent."]
[null,{"$f":"\"From our sample data we see that there is much more variation in the sample data for the Model with a DVD. For example, the range of values for Model with the DVD was \"&DOLLAR(MAX(C2:C6)-MIN(C2:C6))&\" whereas the range for the model without the DVD was \"&DOLLAR(MAX(E2:E6)-MIN(E2:E6))&\". Further, calculating the Coefficient of Variation, we see that the Model without the DVD has \"&DOLLAR(E14,4)&\" of Standard Deviation for every $1.00 of its mean; whereas the Model with a DVD has \"&DOLLAR(C14,4)&\" of Standard Deviation for every $1.00 of its mean.\"","v":"From our sample data we see that there is much more variation in the sample data for the Model with a DVD. For example, the range of values for Model with the DVD was $200.00 whereas the range for the model without the DVD was $70.00. Further, calculating the Coefficient of Variation, we see that the Model without the DVD has $0.0912 of Standard Deviation for every $1.00 of its mean; whereas the Model with a DVD has $0.1809 of Standard Deviation for every $1.00 of its mean."}]
[null,"Other ways to state comparisons with the Coefficient of Variation:"]
[null,{"$f":"\"You could also say it this way: The Model without the DVD has a Standard Deviation that is only \"&TEXT(E14,\"0.00%\")&\" of the value of its mean; whereas, the Model with the DVD has a Standard Deviation that is  \"&TEXT(C14,\"0.00%\")&\" of the value of its mean.\"","v":"You could also say it this way: The Model without the DVD has a Standard Deviation that is only 9.12% of the value of its mean; whereas, the Model with the DVD has a Standard Deviation that is  18.09% of the value of its mean."}]
[null,{"$f":"\"You could also say it this way: For every $1.00 of mean, for the Model with the DVD has a Standard Deviation of \"&DOLLAR(E14,4)&\" and for the Model without the DVD has a Standard Deviation of \"&DOLLAR(C14,4)&\".\"","v":"You could also say it this way: For every $1.00 of mean, for the Model with the DVD has a Standard Deviation of $0.0912 and for the Model without the DVD has a Standard Deviation of $0.1809."}]

{"sheet":"(21)","index":8,"n_rows":13,"n_cols":5,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
["Sample Cities","Grocery Costs",null,"Sample Retirement Areas","Grocery Costs"]
["City 1",33,null,"Retirement Area 1",29]
["City 2",27,null,"Retirement Area 2",32]
["City 3",32,null,"Retirement Area 3",32]
["City 4",38,null,"Retirement Area 4",34]
["City 5",36,null,"Retirement Area 5",34]
["City 6",32,null,"Retirement Area 6",31]
[]
["Mean",{"$f":"AVERAGE(B2:B7)","v":33},null,{"$f":"A9","v":"Mean"},{"$f":"AVERAGE(E2:E7)","v":32}]
["Variance",{"$f":"VAR(B2:B7)","v":14.4},null,{"$f":"A10","v":"Variance"},{"$f":"VAR(E2:E7)","v":3.6}]
["Standard Deviation",{"$f":"_xlfn.STDEV.S(B2:B7)","v":3.7947331922020551},null,{"$f":"A11","v":"Standard Deviation"},{"$f":"_xlfn.STDEV.S(E2:E7)","v":1.8973665961010275}]
[]
["Although the means for the city sample and retirement area sample are very close, the variation in data points for the city sample is twice as large as for the retirement area."]

{"sheet":"(25)","index":9,"n_rows":9,"n_cols":5,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["Sample Data","z = # SD above/below Mean","meaning",null,"check"]
[10,{"$f":"(A2-$B$8)/$B$9","v":-1.25},{"$f":"\"The value of \"&A2&\" is \"&B2&\" standard deviations \"&IF(B2<0,\"below\",\"above\")&\" the mean of \"&$B$8","v":"The value of 10 is -1.25 standard deviations below the mean of 15"},null,{"$f":"STANDARDIZE(A2,$B$8,$B$9)","v":-1.25}]
[20,{"$f":"(A3-$B$8)/$B$9","v":1.25},{"$f":"\"The value of \"&A3&\" is \"&B3&\" standard deviations \"&IF(B3<0,\"below\",\"above\")&\" the mean of \"&$B$8","v":"The value of 20 is 1.25 standard deviations above the mean of 15"},null,{"$f":"STANDARDIZE(A3,$B$8,$B$9)","v":1.25}]
[12,{"$f":"(A4-$B$8)/$B$9","v":-0.75},{"$f":"\"The value of \"&A4&\" is \"&B4&\" standard deviations \"&IF(B4<0,\"below\",\"above\")&\" the mean of \"&$B$8","v":"The value of 12 is -0.75 standard deviations below the mean of 15"},null,{"$f":"STANDARDIZE(A4,$B$8,$B$9)","v":-0.75}]
[17,{"$f":"(A5-$B$8)/$B$9","v":0.5},{"$f":"\"The value of \"&A5&\" is \"&B5&\" standard deviations \"&IF(B5<0,\"below\",\"above\")&\" the mean of \"&$B$8","v":"The value of 17 is 0.5 standard deviations above the mean of 15"},null,{"$f":"STANDARDIZE(A5,$B$8,$B$9)","v":0.5}]
[16,{"$f":"(A6-$B$8)/$B$9","v":0.25},{"$f":"\"The value of \"&A6&\" is \"&B6&\" standard deviations \"&IF(B6<0,\"below\",\"above\")&\" the mean of \"&$B$8","v":"The value of 16 is 0.25 standard deviations above the mean of 15"},null,{"$f":"STANDARDIZE(A6,$B$8,$B$9)","v":0.25}]
[]
["Mean",{"$f":"AVERAGE(A2:A6)","v":15}]
["Standard Deviation",{"$f":"_xlfn.STDEV.S(A2:A6)","v":4}]

{"sheet":"(26)","index":10,"n_rows":10,"n_cols":5,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
["Sample Data"]
["Mean",500]
["SD",100]
[]
["Particular X","z = # SD above/below Mean","meaning",null,"check"]
[520,{"$f":"(A6-$B$2)/$B$3","v":0.2},{"$f":"\"The value of \"&A6&\" is \"&B6&\" standard deviations \"&IF(B6<0,\"below\",\"above\")&\" the mean of \"&$B$2","v":"The value of 520 is 0.2 standard deviations above the mean of 500"},null,{"$f":"STANDARDIZE(A6,$B$2,$B$3)","v":0.2}]
[650,{"$f":"(A7-$B$2)/$B$3","v":1.5},{"$f":"\"The value of \"&A7&\" is \"&B7&\" standard deviations \"&IF(B7<0,\"below\",\"above\")&\" the mean of \"&$B$2","v":"The value of 650 is 1.5 standard deviations above the mean of 500"},null,{"$f":"STANDARDIZE(A7,$B$2,$B$3)","v":1.5}]
[500,{"$f":"(A8-$B$2)/$B$3","v":0},{"$f":"\"The value of \"&A8&\" is \"&B8&\" standard deviations \"&IF(B8<0,\"below\",\"above\")&\" the mean of \"&$B$2","v":"The value of 500 is 0 standard deviations above the mean of 500"},null,{"$f":"STANDARDIZE(A8,$B$2,$B$3)","v":0}]
[450,{"$f":"(A9-$B$2)/$B$3","v":-0.5},{"$f":"\"The value of \"&A9&\" is \"&B9&\" standard deviations \"&IF(B9<0,\"below\",\"above\")&\" the mean of \"&$B$2","v":"The value of 450 is -0.5 standard deviations below the mean of 500"},null,{"$f":"STANDARDIZE(A9,$B$2,$B$3)","v":-0.5}]
[280,{"$f":"(A10-$B$2)/$B$3","v":-2.2000000000000002},{"$f":"\"The value of \"&A10&\" is \"&B10&\" standard deviations \"&IF(B10<0,\"below\",\"above\")&\" the mean of \"&$B$2","v":"The value of 280 is -2.2 standard deviations below the mean of 500"},null,{"$f":"STANDARDIZE(A10,$B$2,$B$3)","v":-2.2000000000000002}]

{"sheet":"(27)","index":11,"n_rows":23,"n_cols":9,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["Sample Data"]
["Mean",30]
["SD",5]
[]
["Chebyshev's Theorem = For any shaped data set, at least (1 - 1/z^2) proportion of the values will lie between +/- z standard deviations of the mean"]
[null,null,"z = # SD above/below Mean"]
[null,"lower",{"$f":"B7&\" z\"","v":"lower z"},"upper",{"$f":"D7&\" z\"","v":"upper z"},"ABS of upper and lower the same?","limits","proportion of the values will lie between +/- z standard deviations of the mean","Meaning"]
["a",20,{"$f":"(B8-$B$2)/$B$3","v":-2},40,{"$f":"(D8-$B$2)/$B$3","v":2},{"$f":"ABS(E8)=ABS(C8)","v":true},{"$f":"B8&\" to \"&D8","v":"20 to 40"},{"$f":"1-1/E8^2","v":0.75},{"$f":"\"At least \"&TEXT(H8,\"0,00%\")&\" of the values lie between \"&B8&\" and \"&D8","v":"At least 075% of the values lie between 20 and 40"}]
["b",15,{"$f":"(B9-$B$2)/$B$3","v":-3},45,{"$f":"(D9-$B$2)/$B$3","v":3},{"$f":"ABS(E9)=ABS(C9)","v":true},{"$f":"B9&\" to \"&D9","v":"15 to 45"},{"$f":"1-1/E9^2","v":0.88888888888888884},{"$f":"\"At least \"&TEXT(H9,\"0,00%\")&\" of the values lie between \"&B9&\" and \"&D9","v":"At least 089% of the values lie between 15 and 45"}]
["c",22,{"$f":"(B10-$B$2)/$B$3","v":-1.6},38,{"$f":"(D10-$B$2)/$B$3","v":1.6},{"$f":"ABS(E10)=ABS(C10)","v":true},{"$f":"B10&\" to \"&D10","v":"22 to 38"},{"$f":"1-1/E10^2","v":0.609375},{"$f":"\"At least \"&TEXT(H10,\"0,00%\")&\" of the values lie between \"&B10&\" and \"&D10","v":"At least 061% of the values lie between 22 and 38"}]
["d",18,{"$f":"(B11-$B$2)/$B$3","v":-2.4},42,{"$f":"(D11-$B$2)/$B$3","v":2.4},{"$f":"ABS(E11)=ABS(C11)","v":true},{"$f":"B11&\" to \"&D11","v":"18 to 42"},{"$f":"1-1/E11^2","v":0.82638888888888884},{"$f":"\"At least \"&TEXT(H11,\"0,00%\")&\" of the values lie between \"&B11&\" and \"&D11","v":"At least 083% of the values lie between 18 and 42"}]
["e",12,{"$f":"(B12-$B$2)/$B$3","v":-3.6},48,{"$f":"(D12-$B$2)/$B$3","v":3.6},{"$f":"ABS(E12)=ABS(C12)","v":true},{"$f":"B12&\" to \"&D12","v":"12 to 48"},{"$f":"1-1/E12^2","v":0.9228395061728395},{"$f":"\"At least \"&TEXT(H12,\"0,00%\")&\" of the values lie between \"&B12&\" and \"&D12","v":"At least 092% of the values lie between 12 and 48"}]
[]
[]
[]
[]
[]
[null,null,"check",null,"check"]
[null,null,{"$f":"STANDARDIZE(B8,$B$2,$B$3)","v":-2},null,{"$f":"STANDARDIZE(D8,$B$2,$B$3)","v":2}]
[null,null,{"$f":"STANDARDIZE(B9,$B$2,$B$3)","v":-3},null,{"$f":"STANDARDIZE(D9,$B$2,$B$3)","v":3}]
[null,null,{"$f":"STANDARDIZE(B10,$B$2,$B$3)","v":-1.6},null,{"$f":"STANDARDIZE(D10,$B$2,$B$3)","v":1.6}]
[null,null,{"$f":"STANDARDIZE(B11,$B$2,$B$3)","v":-2.4},null,{"$f":"STANDARDIZE(D11,$B$2,$B$3)","v":2.4}]
[null,null,{"$f":"STANDARDIZE(B12,$B$2,$B$3)","v":-3.6},null,{"$f":"STANDARDIZE(D12,$B$2,$B$3)","v":3.6}]

{"sheet":"(28)","index":12,"n_rows":200,"n_cols":16,"rows_kept":200,"cut":false,"hidden":false,"merged":[]}
["Data has a bell-shaped distribution, like these ====>",null,null,null,null,null,null,null,null,null,null,null,"Frequency",null,"X","Relative Frequency"]
[null,null,null,null,null,null,null,null,null,null,null,null,2,null,2000,{"$f":"NORMDIST(O2,3000,300,0)","v":5.1409299876370169E-6}]
["Sample Data",null,null,null,null,null,null,null,null,null,null,null,4,null,2010,{"$f":"NORMDIST(O3,3000,300,0)","v":5.7418964635122707E-6}]
["Mean",30,null,null,null,null,null,null,null,null,null,null,6,null,2020,6.4059932311733621E-6]
["SD",5,null,null,null,null,null,null,null,null,null,null,8,null,2030,7.1389615734425603E-6]
[null,null,null,null,null,null,null,null,null,null,null,null,6,null,2040,7.9469606715494682E-6]
[null,null,null,null,null,null,null,null,null,null,null,null,4,null,2050,8.8365865147670191E-6]
["For bell shaped data ==>\nNormal (Empirical) Rule:\nApproximately 68% of values lie between +/- 1 SD\nApproximately 95% of values lie between +/- 2 SD\nApproximately 99% of values lie between +/- 3 SD",null,null,null,null,null,null,null,null,null,null,null,2,null,2060,9.814890401277865E-6]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2070,1.0889396853999729E-5]
[null,"lower",{"$f":"B10&\" z (#SD)\"","v":"lower z (#SD)"},"upper",{"$f":"D10&\" z (#SD)\"","v":"upper z (#SD)"},"ABS of upper and lower the same?","limits","meaning",null,null,null,null,null,null,2080,1.206812076006429E-5]
["a",20,{"$f":"(B11-$B$4)/$B$5","v":-2},40,{"$f":"(D11-$B$4)/$B$5","v":2},{"$f":"ABS(C11)=ABS(E11)","v":true},{"$f":"B11&\" to \"&D11","v":"20 to 40"},{"$f":"VLOOKUP(E11,$H$15:$I$17,2,0)&\" values lie between the values \"&B11&\" and \"&D11","v":"Approximately 95% of values lie between the values 20 and 40"},null,null,null,null,null,null,2090,1.335958352772115E-5]
["b",15,{"$f":"(B12-$B$4)/$B$5","v":-3},45,{"$f":"(D12-$B$4)/$B$5","v":3},{"$f":"ABS(C12)=ABS(E12)","v":true},{"$f":"B12&\" to \"&D12","v":"15 to 45"},{"$f":"VLOOKUP(E12,$H$15:$I$17,2,0)&\" lie between the values \"&B12&\" and \"&D12","v":"Approximately 99% of lie between the values 15 and 45"},null,null,null,null,null,null,2100,1.4772828039793357E-5]
["c",25,{"$f":"(B13-$B$4)/$B$5","v":-1},35,{"$f":"(D13-$B$4)/$B$5","v":1},{"$f":"ABS(C13)=ABS(E13)","v":true},{"$f":"B13&\" to \"&D13","v":"25 to 35"},{"$f":"VLOOKUP(E13,$H$15:$I$17,2,0)&\" lie between the values \"&B13&\" and \"&D13","v":"Approximately 68% of lie between the values 25 and 35"},null,null,null,null,null,null,2110,1.6317432168629774E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2140,2.1843440296711739E-5]
[null,null,"standard deviations above and below the mean",null,null,null,null,1,"Approximately 68% of",null,null,null,null,null,2150,2.4020332548697411E-5]
[null,null,"standard deviations above and below the mean",null,null,null,null,2,"Approximately 95% of",null,null,null,null,null,2160,2.6384838609933229E-5]
[null,null,"standard deviations above and below the mean",null,null,null,null,3,"Approximately 99% of",null,null,null,null,null,2170,2.8949916735929685E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2180,3.17290921844573E-5]
[null,null,"check",null,"check",null,null,null,null,null,null,null,null,null,2190,3.4736449381408632E-5]
[null,null,{"$f":"STANDARDIZE(B11,$B$4,$B$5)","v":-2},null,{"$f":"STANDARDIZE(D11,$B$4,$B$5)","v":2},null,null,null,null,null,null,null,null,null,2200,3.7986620079324806E-5]
[null,null,{"$f":"STANDARDIZE(B12,$B$4,$B$5)","v":-3},null,{"$f":"STANDARDIZE(D12,$B$4,$B$5)","v":3},null,null,null,null,null,null,null,null,null,2210,4.1494767206680685E-5]
[null,null,{"$f":"STANDARDIZE(B13,$B$4,$B$5)","v":-1},null,{"$f":"STANDARDIZE(D13,$B$4,$B$5)","v":1},null,null,null,null,null,null,null,null,null,2220,4.5276564112285379E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2230,4.9348168918754285E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2240,5.3726193712163308E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2250,5.8427668311895131E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2260,6.3469998385500884E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2270,6.8870917698260736E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2280,7.4648434316142994E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2290,8.0820770614091204E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2300,8.7406296979031613E-5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2310,9.4423459138670619E-5]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2350,1.2717541168805993E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2360,1.3662418681740731E-4]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2390,1.6826957860075896E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2400,1.7996988837729353E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2410,1.922700051971094E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2420,2.0518267116449092E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2430,2.1871938258225532E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2440,2.3289025356971723E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2450,2.4770387852997701E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2460,2.6316719433631383E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2470,2.7928534316654915E-4]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2490,3.1349692458962315E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2500,3.3159046264249559E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2510,3.5033879122083387E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2520,3.6973611559818512E-4]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2670,7.2617392344183514E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2680,7.5287609155708167E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2690,7.796933187005432E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2700,8.06569081730478E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2710,8.3344467884886148E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2720,8.6025941967745885E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2730,8.8695083299584945E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2740,9.13454891323428E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2750,9.3970625136767527E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2760,9.6563850920494243E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2770,9.911844689093419E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2780,1.0162764232017239E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2790,1.0408464445558709E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2800,1.0648266850745074E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2810,1.0881496833350865E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2820,1.110748676305999E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2830,1.1325579143491935E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2840,1.1535129772564097E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2850,1.1735510892143318E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2860,1.1926114305598964E-3]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2910,1.2712927182017472E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2920,1.2833562486533798E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2930,1.2940955690784895E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2940,1.3034756465848528E-3]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2970,1.3231751582567059E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2980,1.3268557543798408E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2990,1.3290690245165901E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3000,1.329807601338109E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3010,1.3290690245165901E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3020,1.3268557543798408E-3]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3050,1.3114657203397997E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3060,1.3034756465848528E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3070,1.2940955690784895E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3080,1.2833562486533798E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3090,1.2712927182017472E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3100,1.2579440923099771E-3]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3130,1.2106354441713933E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3140,1.1926114305598964E-3]
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{"sheet":"(29)","index":13,"n_rows":13,"n_cols":12,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
["National Survey"]
[null,"#","Units"]
["Mean time adults sleep per night",6.9,"hours"]
["SD",1.2,"hours"]
[]
[null,"lower",{"$f":"B6&\" z (#SD)\"","v":"lower z (#SD)"},"upper",{"$f":"D6&\" z (#SD)\"","v":"upper z (#SD)"},"ABS of upper and lower the same?","Chebyshev's",null,null,"check",null,"check"]
["a",4.5,{"$f":"(B7-$B$3)/$B$4","v":-2.0000000000000004},9.3000000000000007,{"$f":"(D7-$B$3)/$B$4","v":2.0000000000000004},{"$f":"ABS(E7)=ABS(C7)","v":true},{"$f":"1-1/E7^2","v":0.75000000000000011},{"$f":"\"At least \"&TEXT(G7,\"0.00%\")&\" of adults sleep between \"&B7&\" and \"&D7&\" hours per night/day\"","v":"At least 75.00% of adults sleep between 4.5 and 9.3 hours per night/day"},null,{"$f":"STANDARDIZE(B7,$B$3,$B$4)","v":-2.0000000000000004},null,{"$f":"STANDARDIZE(D7,$B$3,$B$4)","v":2.0000000000000004}]
["b",3.9,{"$f":"(B8-$B$3)/$B$4","v":-2.5000000000000004},9.9,{"$f":"(D8-$B$3)/$B$4","v":2.5},{"$f":"ABS(E8)=ABS(C8)","v":true},{"$f":"1-1/E8^2","v":0.84},{"$f":"\"At least \"&TEXT(G8,\"0.00%\")&\" of adults sleep between \"&B8&\" and \"&D8&\" hours per night/day\"","v":"At least 84.00% of adults sleep between 3.9 and 9.9 hours per night/day"},null,{"$f":"STANDARDIZE(B8,$B$3,$B$4)","v":-2.5000000000000004},null,{"$f":"STANDARDIZE(D8,$B$3,$B$4)","v":2.5}]
[]
["c 1",{"$f":"\"Assuming a Bell-Shaped distribution, approximately \"&TEXT(1-NORMSDIST(C7)*2,\"0.00%\")&\" of adults sleep between \"&B7&\" and \"&D7&\" hours per day/night\"","v":"Assuming a Bell-Shaped distribution, approximately 95.45% of adults sleep between 4.5 and 9.3 hours per day/night"}]
["This one not required ==>\n(we learn this later)",{"$f":"\"Assuming a Bell-Shaped distribution, approximately \"&TEXT(1-NORMSDIST(C8)*2,\"0.00%\")&\" of adults sleep between \"&B8&\" and \"&D8&\" hours per day/night\"","v":"Assuming a Bell-Shaped distribution, approximately 98.76% of adults sleep between 3.9 and 9.9 hours per day/night"}]
[]
["c 2","With the bell-shaped distribution we get about 95% and with a unknown distribution shaped we get a more conservative (smaller) 75%."]

{"sheet":"(30)","index":14,"n_rows":128,"n_cols":12,"rows_kept":128,"cut":false,"hidden":false,"merged":[]}
["Mean regular gas per gallon cost =",2.81,null,null,null,null,"We can do this because the curve is symmetrical"]
["Suppose Sample SD =",0.1]
["Retail price per gallon dstribution is bell shaped"]
[]
[null,null,"lower",{"$f":"C5&\" z (#SD)\"","v":"lower z (#SD)"},"upper",{"$f":"E5&\" z (#SD)\"","v":"upper z (#SD)"},"Total Area Under Curve (Probability)","meaning"]
[null,"a",2.71,{"$f":"(C6-$B$1)/$B$2","v":-1.0000000000000009},2.91,{"$f":"(E6-$B$1)/$B$2","v":1.0000000000000009},{"$f":"D11","v":0.68},{"$f":"IF(G6=\"\",\"\",\"Aproximately \"&TEXT(G6,\"0.00%\")&\" of regular grade gas sold between \"&DOLLAR(C6,2)&\" and \"&DOLLAR(E6,2))","v":"Aproximately 68.00% of regular grade gas sold between $2.71 and $2.91"}]
[null,"b",2.71,{"$f":"(C7-$B$1)/$B$2","v":-1.0000000000000009},3.01,{"$f":"(E7-$B$1)/$B$2","v":1.9999999999999973},{"$f":"E11+E12","v":0.81499999999999995},{"$f":"IF(G7=\"\",\"\",\"Aproximately \"&TEXT(G7,\"0.00%\")&\" of regular grade gas sold between \"&DOLLAR(C7,2)&\" and \"&DOLLAR(E7,2))","v":"Aproximately 81.50% of regular grade gas sold between $2.71 and $3.01"}]
[null,"c",null,null,3.01,{"$f":"(E8-$B$1)/$B$2","v":1.9999999999999973},{"$f":"0.5-E12","v":2.5000000000000022E-2},{"$f":"IF(G8=\"\",\"\",\"Aproximately \"&TEXT(G8,\"0.00%\")&\" of regular grade gas sold above \"&DOLLAR(E8,2))","v":"Aproximately 2.50% of regular grade gas sold above $3.01"}]
[]
[null,null,"# SD","%","Divide by 2"]
[null,null,1,0.68,{"$f":"D11/2","v":0.34}]
[null,null,2,0.95,{"$f":"D12/2","v":0.47499999999999998}]
[null,null,3,0.99,{"$f":"D13/2","v":0.495}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,1,2,3]
["X","Bell Shaped Distribution",{"$f":"\"+/- \"&C26&\"SD \"&VLOOKUP(C26,$K$27:$L$29,2)","v":"+/- 1SD Approximately 68% of Values"},{"$f":"\"+/- \"&D26&\"SD \"&VLOOKUP(D26,$K$27:$L$29,2)","v":"+/- 2SD Approximately 95% of Values"},{"$f":"\"+/- \"&E26&\"SD \"&VLOOKUP(E26,$K$27:$L$29,2)","v":"+/- 3SD Approximately 99% of Values"},null,null,null,null,null,1,"Approximately 68% of Values"]
[{"$f":"B1-B2*5","v":2.31},{"$f":"((1/($B$2*SQRT(2*PI())))*EXP(1)^-((A28-$B$1)^2/(2*$B$2^2)))/100","v":1.4867195147343006E-7},{"$f":"IF(AND($A28>=$B$1-$B$2*C$26,$A28<=$B$1+$B$2*C$26),$B28,\"\")","v":""},"","",null,null,null,null,null,2,"Approximately 95% of Values"]
[{"$f":"A28+0.01","v":2.3199999999999998},{"$f":"((1/($B$2*SQRT(2*PI())))*EXP(1)^-((A29-$B$1)^2/(2*$B$2^2)))/100","v":2.4389607458933393E-7},"","","",null,null,null,null,null,3,"Approximately 99% of Values"]
[{"$f":"A29+0.01","v":2.3299999999999996},3.9612990910319982E-7,"","",""]
[2.3399999999999994,6.3698251788669209E-7,"","",""]
[2.3499999999999992,1.0140852065486364E-6,"","",""]
[2.359999999999999,1.5983741106904734E-6,"","",""]
[2.3699999999999988,2.4942471290052202E-6,"","",""]
[2.3799999999999986,3.8535196742084663E-6,"","",""]
[2.3899999999999983,5.8943067756535666E-6,"","",""]
[2.3999999999999981,8.9261657177125955E-6,"","",""]
[2.4099999999999979,1.3383022576487418E-5,"","",""]
[2.4199999999999977,1.9865547139275486E-5,"","",""]
[2.4299999999999975,2.9194692579143228E-5,"","",""]
[2.4399999999999973,4.247802705507088E-5,"","",""]
[2.4499999999999971,6.1190193011370668E-5,"","",""]
[2.4599999999999969,8.7268269504566401E-5,"","",""]
[2.4699999999999966,1.2322191684728778E-4,"","",""]
[2.4799999999999964,1.7225689390534764E-4,"","",""]
[2.4899999999999962,2.3840882014645521E-4,"","",""]
[2.499999999999996,3.2668190561995126E-4,"","",""]
[2.5099999999999958,4.4318484119374444E-4,{"$f":"IF(AND($A48>=$B$1-$B$2*C$26,$A48<=$B$1+$B$2*C$26),$B48,\"\")","v":""},"",4.4318484119374444E-4]
[2.5199999999999956,5.9525324197750825E-4,"","",5.9525324197750825E-4]
[2.5299999999999954,7.915451582978934E-4,"","",7.915451582978934E-4]
[2.5399999999999952,1.0420934814421225E-3,"","",1.0420934814421225E-3]
[2.5499999999999949,1.3582969233683823E-3,"","",1.3582969233683823E-3]
[2.5599999999999947,1.7528300493566211E-3,"","",1.7528300493566211E-3]
[2.5699999999999945,2.2394530294839927E-3,"","",2.2394530294839927E-3]
[2.5799999999999943,2.8327037741597439E-3,"","",2.8327037741597439E-3]
[2.5899999999999941,3.5474592846226789E-3,"","",3.5474592846226789E-3]
[2.5999999999999939,4.3983595980421506E-3,"","",4.3983595980421506E-3]
[2.6099999999999937,5.3990966513181148E-3,"","",5.3990966513181148E-3]
[2.6199999999999934,6.5615814774668381E-3,"",6.5615814774668381E-3,6.5615814774668381E-3]
[2.6299999999999932,7.8950158300884494E-3,"",7.8950158300884494E-3,7.8950158300884494E-3]
[2.639999999999993,9.4049077376875713E-3,"",9.4049077376875713E-3,9.4049077376875713E-3]
[2.6499999999999928,1.1092083467944271E-2,"",1.1092083467944271E-2,1.1092083467944271E-2]
[2.6599999999999926,1.2951759566587728E-2,"",1.2951759566587728E-2,1.2951759566587728E-2]
[2.6699999999999924,1.4972746563572881E-2,"",1.4972746563572881E-2,1.4972746563572881E-2]
[2.6799999999999922,1.7136859204778983E-2,"",1.7136859204778983E-2,1.7136859204778983E-2]
[2.689999999999992,1.9418605498319409E-2,"",1.9418605498319409E-2,1.9418605498319409E-2]
[2.6999999999999917,2.1785217703253066E-2,"",2.1785217703253066E-2,2.1785217703253066E-2]
[2.7099999999999915,2.4197072451912275E-2,{"$f":"IF(AND($A68>=$B$1-$B$2*C$26,$A68<=$B$1+$B$2*C$26),$B68,\"\")","v":""},2.4197072451912275E-2,2.4197072451912275E-2]
[2.7199999999999913,2.6608524989873393E-2,2.6608524989873393E-2,2.6608524989873393E-2,2.6608524989873393E-2]
[2.7299999999999911,2.8969155276146203E-2,2.8969155276146203E-2,2.8969155276146203E-2,2.8969155276146203E-2]
[2.7399999999999909,3.1225393336674127E-2,3.1225393336674127E-2,3.1225393336674127E-2,3.1225393336674127E-2]
[2.7499999999999907,3.3322460289178089E-2,3.3322460289178089E-2,3.3322460289178089E-2,3.3322460289178089E-2]
[2.7599999999999905,3.5206532676428259E-2,3.5206532676428259E-2,3.5206532676428259E-2,3.5206532676428259E-2]
[2.7699999999999902,3.6827014030330889E-2,3.6827014030330889E-2,3.6827014030330889E-2,3.6827014030330889E-2]
[2.77999999999999,3.8138781546051256E-2,3.8138781546051256E-2,3.8138781546051256E-2,3.8138781546051256E-2]
[2.7899999999999898,3.9104269397544786E-2,3.9104269397544786E-2,3.9104269397544786E-2,3.9104269397544786E-2]
[2.7999999999999896,3.9695254747700762E-2,3.9695254747700762E-2,3.9695254747700762E-2,3.9695254747700762E-2]
[2.8099999999999894,3.9894228040143268E-2,3.9894228040143268E-2,3.9894228040143268E-2,3.9894228040143268E-2]
[2.8199999999999892,3.9695254747701615E-2,3.9695254747701615E-2,3.9695254747701615E-2,3.9695254747701615E-2]
[2.829999999999989,3.9104269397546458E-2,3.9104269397546458E-2,3.9104269397546458E-2,3.9104269397546458E-2]
[2.8399999999999888,3.8138781546053706E-2,3.8138781546053706E-2,3.8138781546053706E-2,3.8138781546053706E-2]
[2.8499999999999885,3.6827014030334032E-2,3.6827014030334032E-2,3.6827014030334032E-2,3.6827014030334032E-2]
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[2.8699999999999881,3.332246028918235E-2,3.332246028918235E-2,3.332246028918235E-2,3.332246028918235E-2]
[2.8799999999999879,3.122539333667879E-2,3.122539333667879E-2,3.122539333667879E-2,3.122539333667879E-2]
[2.8899999999999877,2.896915527615114E-2,2.896915527615114E-2,2.896915527615114E-2,2.896915527615114E-2]
[2.8999999999999875,2.66085249898785E-2,2.66085249898785E-2,2.66085249898785E-2,2.66085249898785E-2]
[2.9099999999999873,2.4197072451917438E-2,{"$f":"IF(AND($A88>=$B$1-$B$2*C$26,$A88<=$B$1+$B$2*C$26),$B88,\"\")","v":2.4197072451917438E-2},2.4197072451917438E-2,2.4197072451917438E-2]
[2.9199999999999871,2.1785217703258173E-2,"",2.1785217703258173E-2,2.1785217703258173E-2]
[2.9299999999999868,1.9418605498324377E-2,"",1.9418605498324377E-2,1.9418605498324377E-2]
[2.9399999999999866,1.7136859204783732E-2,"",1.7136859204783732E-2,1.7136859204783732E-2]
[2.9499999999999864,1.497274656357735E-2,"",1.497274656357735E-2,1.497274656357735E-2]
[2.9599999999999862,{"$f":"((1/($B$2*SQRT(2*PI())))*EXP(1)^-((A93-$B$1)^2/(2*$B$2^2)))/100","v":1.2951759566591869E-2},"",1.2951759566591869E-2,1.2951759566591869E-2]
[{"$f":"A93+0.01","v":2.969999999999986},1.1092083467948058E-2,"",1.1092083467948058E-2,1.1092083467948058E-2]
[2.9799999999999858,9.4049077376909766E-3,"",9.4049077376909766E-3,9.4049077376909766E-3]
[2.9899999999999856,7.8950158300914782E-3,"",7.8950158300914782E-3,7.8950158300914782E-3]
[2.9999999999999853,6.5615814774694949E-3,"",6.5615814774694949E-3,6.5615814774694949E-3]
[3.0099999999999851,5.3990966513204177E-3,"",5.3990966513204177E-3,5.3990966513204177E-3]
[3.0199999999999849,4.3983595980441196E-3,"","",4.3983595980441196E-3]
[3.0299999999999847,3.5474592846243425E-3,"","",3.5474592846243425E-3]
[3.0399999999999845,2.8327037741611321E-3,"","",2.8327037741611321E-3]
[3.0499999999999843,2.2394530294851393E-3,"","",2.2394530294851393E-3]
[3.0599999999999841,1.7528300493575553E-3,"","",1.7528300493575553E-3]
[3.0699999999999839,1.358296923369135E-3,"","",1.358296923369135E-3]
[3.0799999999999836,1.0420934814427216E-3,"","",1.0420934814427216E-3]
[3.0899999999999834,7.9154515829836557E-4,"","",7.9154515829836557E-4]
[3.0999999999999832,5.9525324197787666E-4,"","",5.9525324197787666E-4]
[3.109999999999983,4.4318484119402785E-4,{"$f":"IF(AND($A108>=$B$1-$B$2*C$26,$A108<=$B$1+$B$2*C$26),$B108,\"\")","v":""},"",4.4318484119402785E-4]
[3.1199999999999828,3.266819056201674E-4,"","",""]
[3.1299999999999826,2.3840882014661784E-4,"","",""]
[3.1399999999999824,1.7225689390546882E-4,"","",""]
[3.1499999999999821,1.2322191684737706E-4,"","",""]
[3.1599999999999819,8.7268269504631508E-5,"","",""]
[3.1699999999999817,6.1190193011417628E-5,"","",""]
[3.1799999999999815,4.2478027055104348E-5,"","",""]
[3.1899999999999813,2.9194692579166877E-5,"","",""]
[3.1999999999999811,1.9865547139292003E-5,"","",""]
[3.2099999999999809,1.3383022576498827E-5,"","",""]
[3.2199999999999807,8.9261657177203967E-6,"","",""]
[3.2299999999999804,5.8943067756588537E-6,"","",""]
[3.2399999999999802,3.853519674212006E-6,"","",""]
[3.24999999999998,2.4942471290075601E-6,"","",""]
[3.2599999999999798,1.5983741106920068E-6,"","",""]
[3.2699999999999796,1.0140852065496307E-6,"","",""]
[3.2799999999999794,6.3698251788733022E-7,"","",""]
[3.2899999999999792,3.9612990910360513E-7,"","",""]
[3.299999999999979,2.4389607458958872E-7,"","",""]
[3.3099999999999787,1.4867195147358849E-7,"","",""]

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["SampleData",null,"by hand",null,"position","Proportion",null,null,"Excel 5-Number Summary"]
[15,null,{"$f":"H2","v":"MIN"},{"$f":"MIN(A2:A9)","v":15},null,null,null,"MIN",{"$f":"_xlfn.QUARTILE.INC($A$2:$A$9,J2)","v":15},0,null,{"$f":"_xlfn.QUARTILE.EXC($A$2:$A$9,J2)","v":{"$error":"#NUM!"}}]
[20,null,"Quartile1",{"$f":"AVERAGE(A3:A4)","v":22.5},{"$f":"COUNT($A$2:$A$9)*F3","v":2},0.25,null,"Quartile1",{"$f":"_xlfn.QUARTILE.INC($A$2:$A$9,J3)","v":23.75},1,null,{"$f":"_xlfn.QUARTILE.EXC($A$2:$A$9,J3)","v":21.25}]
[25,null,"Quartile2",{"$f":"MEDIAN(A2:A9)","v":26},null,null,null,"Quartile2",26,2,null,26]
[25,null,"Quartile3",{"$f":"AVERAGE(A7:A8)","v":29},{"$f":"COUNT($A$2:$A$9)*F5","v":6},0.75,null,"Quartile3",28.5,3,null,29.5]
[27,null,"MAX",{"$f":"MAX(A2:A9)","v":34},null,null,null,"MAX",34,4,null,{"$error":"#NUM!"}]
[28,null,"Interquartile Range",{"$f":"D5-D3","v":6.5},null,null,null,"Interquartile Range",{"$f":"I5-I3","v":4.75}]
[30,null,"Lower Limit",{"$f":"D3-1.5*D7","v":12.75}," Quartile 1 - 1.5*Interquartile Range",null,null,"Lower Limit",{"$f":"I3-1.5*I7","v":16.625}]
[34,null,"Higher Limit",{"$f":"D5+1.5*D7","v":38.75},"Quartile 3 + 1.5*Interquartile Range",null,null,"Higher Limit",{"$f":"I5+1.5*I7","v":35.625}]
[null,null,"Smallest inside lower limit",{"$f":"D2","v":15},null,null,null,"Smallest inside lower limit",{"$f":"MIN(IF(A2:A9>I8,A2:A9))","v":20}]
[null,null,"Biggest inside lower limit",{"$f":"D6","v":34},null,null,null,"Biggest inside lower limit",{"$f":"MAX(IF(A2:A9<I9,A2:A9))","v":34}]
[]
[]
[]
[null,null,{"$f":"C2","v":"MIN"},{"$f":"D2-D1","v":15}]
[null,null,{"$f":"C3","v":"Quartile1"},{"$f":"D3-D2","v":7.5}]
[null,null,{"$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"},{"$f":"D6-D5","v":5}]
[null,null,"Mean"]
[null,null,{"$f":"AVERAGE(A2:A9)","v":25.5},1]

{"sheet":"(42)","index":16,"n_rows":34,"n_cols":14,"rows_kept":34,"cut":false,"hidden":true,"merged":[]}
[null,null,null,null,null,null,null,null,null,null,null,null,"Label",{"$f":"E4&\" = \"&F4&CHAR(10)&E5&\" = \"&F5&CHAR(10)&E6&\" = \"&F6&CHAR(10)&E7&\" = \"&F7&CHAR(10)&E8&\" = \"&F8","v":"Min  = 30\nQuartile 1 = 50.5\nQuartile 2 = 66\nQuartile 3 = 87.75\nMax = 208"}]
["Team","Payroll",null,null,null,null,null,"COUNT",{"$f":"COUNT(B3:B32)","v":30}]
["Tampa Bay",30,null,null,"Excel",null,null,"by hand"]
["Kansas City",37,null,0,"Min ",{"$f":"QUARTILE($B$3:$B$32,D4)","v":30},null,null,"i","roundup","Value"]
["Pittsburgh",38,null,1,"Quartile 1",{"$f":"QUARTILE($B$3:$B$32,D5)","v":50.5},null,0.25,{"$f":"$I$2*H5","v":7.5},{"$f":"ROUNDUP(I5,0)","v":8},{"$f":"INDEX($B$3:$B$32,J5)","v":49}]
["Milwaukee",40,null,2,"Quartile 2",{"$f":"QUARTILE($B$3:$B$32,D6)","v":66},null,0.75,{"$f":"$I$2*H6","v":22.5},{"$f":"ROUNDUP(I6,0)","v":23},{"$f":"INDEX($B$3:$B$32,J6)","v":88}]
["Cleveland",42,null,3,"Quartile 3",{"$f":"QUARTILE($B$3:$B$32,D7)","v":87.75}]
["Toronto",46,null,4,"Max",{"$f":"QUARTILE($B$3:$B$32,D8)","v":208}]
["Colorado",48,null,null,null,null,null,null,"Interquartile range ",{"$f":"K6-K5","v":39}]
["Washington",49,null,null,"Chart Data",null,null,null,"Lower Limit",{"$f":"K5-1.5*$J$9","v":-9.5}," Quartile 1 - 1.5*Interquartile Range"]
["Oakland",55,null,null,null,{"$f":"F3-F2","v":0},null,null,"Higher Limit",{"$f":"K6+1.5*$J$9","v":146.5},"Quartile 3 + 1.5*Interquartile Range"]
["Minnesota",56,null,null,{"$f":"E4","v":"Min "},30,null,null,"Smallest inside lower limit",{"$f":"B3","v":30}]
["Texas",56,null,null,{"$f":"E5","v":"Quartile 1"},20.5,null,null,"Biggest inside lower limit",{"$f":"B31","v":124}]
["Florida",60,null,null,{"$f":"E6","v":"Quartile 2"},15.5,null,null,"See by hand drawing below ==>>"]
["Arizona",62,null,null,{"$f":"E7","v":"Quartile 3"},21.75]
["Cincinnati",62,null,null,{"$f":"E8","v":"Max"},120.25]
["San Diego",63,null,null,"Interquartile range",{"$f":"F7-F5","v":37.25}]
["Detroit",69,null,null,"Lower Limit",{"$f":"F5- 1.5*$F$17","v":-5.375}," Quartile 1 - 1.5*Interquartile Range"]
["Baltimore",74,null,null,"Higher Limit",{"$f":"F7+1.5*$F$17","v":143.625},"Quartile 3 + 1.5*Interquartile Range"]
["Chi White Sox",75,null,null,"Smallest inside lower limit",{"$f":"INDEX($B$3:$B$32,MATCH(IF(F18>0,0,MIN(B3:B32)),$B$3:$B$32))","v":30}]
["Houston",77,null,null,"Biggest inside lower limit",{"$f":"INDEX($B$3:$B$32,MATCH(F19,$B$3:$B$32))","v":124}]
["LA Dodgers",83,null,null,"Upper Bar %",{"$f":"(F21-F7)","v":36.25}]
["Atlanta",86,null,null,"Outlier",1,{"$f":"B32","v":208}]
["Chi Cubs",87,null,null,"Mean",{"$f":"AVERAGE(B3:B32)","v":73.066666666666663}]
["Seattle",88]
["San Francisco",90]
["St. Louis",92]
["Philadelphia",96]
["LA Angles",98]
["NY Mets",101]
["Boston",124]
["NY Yankees",208]
[]
[{"$f":"A32&\" at \"&DOLLAR(B32)","v":"NY Yankees at $208.00"}]

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[" 2003 Ave Visa charge",1838]
[]
["No","SampleData",null,null,null,null,"Excel",null,"By Hand"]
[1,170,null,"a",null,"Mean",{"$f":"AVERAGE(sccd)","v":1800}]
[2,236,null,"a",null,"Median",{"$f":"MEDIAN(sccd)","v":1351}]
[3,316,null,null,0,"Min",{"$f":"_xlfn.QUARTILE.INC(sccd,E6)","v":170},null,"Value","position"]
[4,387,null,"b",1,"Quartile1",{"$f":"_xlfn.QUARTILE.INC(sccd,E7)","v":606},null,{"$f":"VLOOKUP(ROUNDUP(J7,0),$A$4:$B$18,2)","v":387},{"$f":"COUNT(sccd)*K7","v":3.75},0.25]
[5,825,null,"b",2,"Quartile2",{"$f":"_xlfn.QUARTILE.INC(sccd,E8)","v":1351}]
[6,991,null,null,3,"Quartile3",{"$f":"_xlfn.QUARTILE.INC(sccd,E9)","v":1699},null,{"$f":"VLOOKUP(ROUNDUP(J9,0),$A$4:$B$18,2)","v":1710},{"$f":"COUNT(sccd)*K9","v":11.25},0.75]
[7,1333,null,null,4,"Max",{"$f":"_xlfn.QUARTILE.INC(sccd,E10)","v":7450}]
[8,1351,null,"c",null,"Range",{"$f":"G10-G6","v":7280}]
[9,1428,null,"c",null,"Interquartile range",{"$f":"G9-G7","v":1093},null,{"$f":"I9-I7","v":1323}]
[10,1584,null,"d",null,"Sample Variance",{"$f":"_xlfn.VAR.S(sccd)","v":3675303}]
[11,1688,null,"d",null,"Sample SD",{"$f":"_xlfn.STDEV.S(sccd)","v":1917.1079781796329}]
[12,1710,null,null,null,"Chebyshev's",{"$f":"\"75% of values lie between \"&IF(G4-G14*2<0,0,G4-G14*2)&\" and \"&G4+G14*2","v":"75% of values lie between 0 and 5634.21595635927"}]
[13,3396,null,null,null,"Empirical",{"$f":"\"68% of values lie between 0 and \"&G4+G14","v":"68% of values lie between 0 and 3717.10797817963"}]
[14,4135,null,"e",null,"Skew",{"$f":"SKEW(sccd)","v":2.1195274576903658}]
[15,7450,null,null,null,null,"I would expect positive skew because some large values are pulling the mean up"]
[]
[null,null,null,"f","X","z # SD","z = Outlier > 3","Outlier Limit = Q1 - 1.5*Interquartile range","Outlier Limit = Q3 + 1.5*Interquartile range"]
[null,null,null,null,{"$f":"B4","v":170},{"$f":"(B4-$G$4)/$G$14","v":-0.85023901551322478},{"$f":"F21>3","v":false},{"$f":"IF($I$7-1.5*$I$12<0,0,$I$7-1.5*$I$12)>E21","v":false},{"$f":"$I$9+1.5*$I$12<E21","v":false}]
[null,null,null,null,236,-0.81581215967035803,false,{"$f":"IF($I$7-1.5*$I$12<0,0,$I$7-1.5*$I$12)>E22","v":false},false]
[null,null,null,null,316,-0.77408263743658012,false,false,false]
[null,null,null,null,387,-0.73704768645410224,false,false,false]
[null,null,null,null,825,-0.50857855222416826,false,false,false]
[null,null,null,null,991,-0.42198979358907907,false,false,false]
[null,null,null,null,1333,-0.24359608603967853,false,false,false]
[null,null,null,null,1351,-0.23420694353707849,false,false,false]
[null,null,null,null,1428,-0.19404227838706725,false,false,false]
[null,null,null,null,1584,-0.11266971003120034,false,false,false]
[null,null,null,null,1688,-5.8421331127289068E-2,false,false,false]
[null,null,null,null,1710,-4.6945712513000143E-2,false,false,false]
[null,null,null,null,3396,0.83250396856386921,false,false,false]
[null,null,null,null,4135,1.2179804301983925,false,false,true]
[null,null,null,null,7450,2.9471475077605644,false,false,true]