商務(wù)與經(jīng)濟(jì)統(tǒng)計第2章A課件

StatisticsforBusiness

andEconomicsAndersonSweeneyWilliamsSlidesbyJohnLoucksSt.Edward’sUniversityStatisticsforBusiness

andEcChapter2,PartA

DescriptiveStatistics:

TabularandGraphicalPresentationsSummarizingCategoricalDataSummarizingQuantitativeData

Categoricaldatauselabelsornamestoidentifycategoriesoflikeitems.

Quantitativedataarenumericalvaluesthatindicatehowmuchorhowmany.Chapter2,PartA

DescriptiveSummarizingCategoricalDataFrequencyDistributionRelativeFrequencyDistributionPercentFrequencyDistributionBarChartPieChartSummarizingCategoricalDataFrAfrequencydistributionisatabularsummaryofdatashowingthefrequency(ornumber)ofitemsineachofseveralnon-overlappingclasses.Theobjectiveistoprovideinsightsaboutthedatathatcannotbequicklyobtainedbylookingonlyattheoriginaldata.FrequencyDistributionAfrequencydistributionisa

GuestsstayingatMaradaInnwereaskedtoratethequalityoftheiraccommodationsasbeingexcellent,aboveaverage,average,belowaverage,orpoor.Theratingsprovidedbyasampleof20guestsare:

BelowAverageAboveAverageAboveAverageAverageAboveAverageAverageAboveAverage

AverageAboveAverageBelowAveragePoorExcellentAboveAverageAverage

AboveAverageAboveAverageBelowAveragePoorAboveAverageAverageFrequencyDistributionExample:MaradaInn GuestsstayingatMaradaInnFrequencyDistribution

Poor BelowAverageAverage AboveAverageExcellent

2 3 5 9

1Total 20RatingFrequencyExample:MaradaInnFrequencyDistributionTherelativefrequencyofaclassisthefractionorproportionofthetotalnumberofdataitemsbelongingtotheclass.Arelativefrequencydistributionisatabularsummaryofasetofdatashowingtherelativefrequencyforeachclass.RelativeFrequencyDistributionTherelativefrequencyofacPercentFrequencyDistributionThepercentfrequencyofaclassistherelativefrequencymultipliedby100.A

percentfrequencydistributionisatabularsummaryofasetofdatashowingthepercentfrequencyforeachclass.PercentFrequencyDistributionRelativeFrequencyand

PercentFrequencyDistributions

PoorBelowAverageAverageAboveAverageExcellent .10 .15 .25 .45

.05Total 1.0010152545

5100RelativeFrequencyPercentFrequencyRating.10(100)=101/20=.05Example:MaradaInnRelativeFrequencyand

PercentBarChartAbarchartisagraphicaldevicefordepictingqualitativedata.Ononeaxis(usuallythehorizontalaxis),wespecifythelabelsthatareusedforeachoftheclasses.Afrequency,relativefrequency,orpercentfrequencyscalecanbeusedfortheotheraxis(usuallytheverticalaxis).Usingabaroffixedwidthdrawnaboveeachclasslabel,weextendtheheightappropriately.Thebarsareseparatedtoemphasizethefactthateachclassisaseparatecategory.BarChartAbarchartisagPoorBelowAverageAverageAboveAverageExcellentFrequencyRatingBarChart12345678910MaradaInnQualityRatingsPoorBelowAverageAboveExcellenParetoDiagramInqualitycontrol,barchartsareusedtoidentifythemostimportantcausesofproblems.Whenthebarsarearrangedindescendingorderofheightfromlefttoright(withthemostfrequentlyoccurringcauseappearingfirst)thebarchartiscalledaParetodiagram.Thisdiagramisnamedforitsfounder,VilfredoPareto,anItalianeconomist.ParetoDiagramInqualitycoPieChartThepiechartisacommonlyusedgraphicaldeviceforpresentingrelativefrequencyandpercent

frequencydistributionsforcategoricaldata.Firstdrawacircle;thenusetherelativefrequenciestosubdividethecircleintosectorsthatcorrespondtotherelativefrequencyforeachclass.Sincethereare360degreesinacircle,aclasswitharelativefrequencyof.25wouldconsume.25(360)=90degreesofthecircle.PieChartThepiechartisa

BelowAverage15%Average25%AboveAverage45%Poor10%Excellent5%

MaradaInn

QualityRatingsPieChartBelowAverageAbovePoorExceInsightsGainedfromthePrecedingPieChartExample:MaradaInnOne-halfofthecustomerssurveyedgaveMaradaaqualityratingof“aboveaverage”or“excellent”(lookingattheleftsideofthepie).Thismightpleasethemanager.Foreachcustomerwhogavean“excellent”rating,thereweretwocustomerswhogavea“poor”rating(lookingatthetopofthepie).Thisshoulddispleasethemanager.InsightsGainedfromthePreceSummarizingQuantitativeDataFrequencyDistributionRelativeFrequencyandPercentFrequencyDistributionsDotPlotHistogramCumulativeDistributionsOgiveSummarizingQuantitativeDataF ThemanagerofHudsonAutowouldliketogainabetterunderstandingofthecostofpartsusedintheenginetune-upsperformedintheshop.Sheexamines50customerinvoicesfortune-ups.Thecostsofparts,roundedtothenearestdollar,arelistedonthenextslide.Example:HudsonAutoRepairFrequencyDistribution ThemanagerofHudsonAutowoSampleofPartsCost($)for50Tune-upsFrequencyDistributionExample:HudsonAutoRepairSampleofPartsCost($)for50FrequencyDistribution2.Determinethewidthofeachclass.3.Determinetheclasslimits.1.Determinethenumberofnon-overlappingclasses.Thethreestepsnecessarytodefinetheclassesforafrequencydistributionwithquantitativedataare:FrequencyDistribution2.DetFrequencyDistributionGuidelinesforDeterminingtheNumberofClassesUsebetween5and20classes.Datasetswithalargernumberofelementsusuallyrequirealargernumberofclasses.Smallerdatasetsusuallyrequirefewerclasses.Thegoalistouseenoughclassestoshowthevariationinthedata,butnotsomanyclassesthatsomecontainonlyafewdataitems.FrequencyDistributionGuidelinFrequencyDistributionGuidelinesforDeterminingtheWidthofEachClassUseclassesofequalwidth.ApproximateClassWidth=Makingtheclassesthesamewidthreducesthechanceofinappropriateinterpretations.FrequencyDistributionGuidelinNoteonNumberofClassesandClassWidthInpractice,thenumberofclassesandtheappropriateclasswidtharedeterminedbytrialanderror.Onceapossiblenumberofclassesischosen,theappropriateclasswidthisfound.Theprocesscanberepeatedforadifferentnumberofclasses.FrequencyDistributionUltimately,theanalystusesjudgmenttodeterminethecombinationofthenumberofclassesandclasswidththatprovidesthebestfrequencydistributionforsummarizingthedata.NoteonNumberofClassesandFrequencyDistributionGuidelinesforDeterminingtheClassLimitsClasslimitsmustbechosensothateachdataitembelongstooneandonlyoneclass.Thelowerclasslimitidentifiesthesmallestpossibledatavalueassignedtotheclass.Theupperclasslimitidentifiesthelargestpossibledatavalueassignedtotheclass.Theappropriatevaluesfortheclasslimitsdependonthelevelofaccuracyofthedata.Anopen-endclassrequiresonlyalowerclasslimitoranupperclasslimit.FrequencyDistributionGuidelinFrequencyDistributionIfwechoosesixclasses:

50-59 60-6970-79 80-89 90-99 100-109

2131677

5Total50PartsCost($)FrequencyApproximateClassWidth=(109-52)/6=9.510Example:HudsonAutoRepairFrequencyDistributionIfwechRelativeFrequencyand

PercentFrequencyDistributions

50-59 60-6970-79 80-89 90-99 100-109PartsCost($)

.04.26.32.14.14

.10Total1.00RelativeFrequency

42632141410100PercentFrequency2/50.04(100)Example:HudsonAutoRepairPercentfrequencyistherelativefrequencymultipliedby100.RelativeFrequencyand

PercentOnly4%ofthepartscostsareinthe$50-59class.Thegreatestpercentage(32%oralmostone-third)ofthepartscostsareinthe$70-79class.30%ofthepartscostsareunder$70.10%ofthepartscostsare$100ormore.InsightsGainedfromthe%FrequencyDistribution:RelativeFrequencyand

PercentFrequencyDistributionsExample:HudsonAutoRepairOnly4%ofthepartscostsaDotPlotOneofthesimplestgraphicalsummariesofdataisadotplot.Ahorizontalaxisshowstherangeofdatavalues.Theneachdatavalueisrepresentedbyadotplacedabovetheaxis.DotPlotOneofthesimplestgrDotPlot50

60

70

80

90

100

110Cost($)Tune-upPartsCostExample:HudsonAutoRepairDotPlot5060HistogramAnothercommongraphicalpresentationofquantitativedataisahistogram.Thevariableofinterestisplacedonthehorizontalaxis.Arectangleisdrawnaboveeachclassintervalwithitsheightcorrespondingtotheinterval’sfrequency,

relativefrequency,orpercentfrequency.Unlikeabargraph,ahistogramhasnonatural

separationbetweenrectanglesofadjacentclasses.HistogramAnothercommongraHistogram24681012141618PartsCost($)Frequency50-5960-6970-79

80-8990-99100-110Tune-upPartsCostExample:HudsonAutoRepairHistogram24681012141618PartsSymmetricHistogramsShowingSkewnessRelativeFrequency.05.10.15.20.25.30.350LefttailisthemirrorimageoftherighttailExamples:heightsandweightsofpeopleSymmetricHistogramsShowingSkHistogramsShowingSkewnessModeratelySkewedLeftRelativeFrequency.05.10.15.20.25.30.350AlongertailtotheleftExample:examscoresHistogramsShowingSkewnessModModeratelyRightSkewedHistogramsShowingSkewnessRelativeFrequency.05.10.15.20.25.30.350ALongertailtotherightExample:housingvaluesModeratelyRightSkewedHistogrHistogramsShowingSkewnessHighlySkewedRightRelativeFrequency.05.10.15.20.25.30.350AverylongtailtotherightExample:executivesalariesHistogramsShowingSkewnessHig

Cumulativefrequencydistribution

-showsthe

numberofitemswithvalueslessthanorequaltotheupperlimitofeachclass..

Cumulativerelativefrequencydistribution–showstheproportionofitemswithvalueslessthanorequaltotheupperlimitofeachclass.CumulativeDistributions

Cumulativepercentfrequencydistribution–showsthepercentageofitemswithvalueslessthanorequaltotheupperlimitofeachclass.CumulativefrequencydistribuCumulativeDistributionsThelastentryinacumulativefrequencydistributionalwaysequalsthetotalnumberofobservations.Thelastentryinacumulativerelativefrequencydistributionalwaysequals1.00.Thelastentryinacumulativepercentfrequencydistributionalwaysequals100.CumulativeDistributionsTheCumulativeDistributionsHudsonAutoRepair

<59

<69

<79

<89

<99 <109Cost($)CumulativeFrequencyCumulativeRelativeFrequencyCumulativePercentFrequency

21531384550

.04.30.62.76.901.00

4306276901002+1315/50.30(100)CumulativeDistributionsHudsonOgiveAnogiveisagraphofacumulativedistribution.Thedatavaluesareshownonthehorizontalaxis.Shownontheverticalaxisarethe:cumulativefrequencies,orcumulativerelativefrequencies,orcumulativepercentfrequenciesThefrequency(oneoftheabove)ofeachclassisplottedasapoint.Theplottedpointsareconnectedbystraightlines.OgiveAnogiveisagraphofaBecausetheclasslimitsfortheparts-costdataare50-59,60-69,andsoon,thereappeartobeone-unitgapsfrom59to60,69to70,andsoon.OgiveThesegapsareeliminatedbyplottingpointshalfwaybetweentheclasslimits.Thus,59.5isusedforthe50-59class,69.5isusedforthe60-69class,andsoon.HudsonAutoRepairOgiveHudsonAutoRepair

PartsCost($)20406080100CumulativePercentFrequency5060708090100110(89.5,76)OgivewithCumulativePercentFrequenciesTune-upPartsCostExample:HudsonAutoRepairParts20406080100CumulativePEndofChapter2,PartAEndofChapter2,PartAStatisticsforBusiness

andEconomicsAndersonSweeneyWilliamsSlidesbyJohnLoucksSt.Edward’sUniversityStatisticsforBusiness

andEcChapter2,PartA

DescriptiveStatistics:

TabularandGraphicalPresentationsSummarizingCategoricalDataSummarizingQuantitativeData

Categoricaldatauselabelsornamestoidentifycategoriesoflikeitems.

Quantitativedataarenumericalvaluesthatindicatehowmuchorhowmany.Chapter2,PartA

DescriptiveSummarizingCategoricalDataFrequencyDistributionRelativeFrequencyDistributionPercentFrequencyDistributionBarChartPieChartSummarizingCategoricalDataFrAfrequencydistributionisatabularsummaryofdatashowingthefrequency(ornumber)ofitemsineachofseveralnon-overlappingclasses.Theobjectiveistoprovideinsightsaboutthedatathatcannotbequicklyobtainedbylookingonlyattheoriginaldata.FrequencyDistributionAfrequencydistributionisa

GuestsstayingatMaradaInnwereaskedtoratethequalityoftheiraccommodationsasbeingexcellent,aboveaverage,average,belowaverage,orpoor.Theratingsprovidedbyasampleof20guestsare:

BelowAverageAboveAverageAboveAverageAverageAboveAverageAverageAboveAverage

AverageAboveAverageBelowAveragePoorExcellentAboveAverageAverage

AboveAverageAboveAverageBelowAveragePoorAboveAverageAverageFrequencyDistributionExample:MaradaInn GuestsstayingatMaradaInnFrequencyDistribution

Poor BelowAverageAverage AboveAverageExcellent

2 3 5 9

1Total 20RatingFrequencyExample:MaradaInnFrequencyDistributionTherelativefrequencyofaclassisthefractionorproportionofthetotalnumberofdataitemsbelongingtotheclass.Arelativefrequencydistributionisatabularsummaryofasetofdatashowingtherelativefrequencyforeachclass.RelativeFrequencyDistributionTherelativefrequencyofacPercentFrequencyDistributionThepercentfrequencyofaclassistherelativefrequencymultipliedby100.A

percentfrequencydistributionisatabularsummaryofasetofdatashowingthepercentfrequencyforeachclass.PercentFrequencyDistributionRelativeFrequencyand

PercentFrequencyDistributions

PoorBelowAverageAverageAboveAverageExcellent .10 .15 .25 .45

.05Total 1.0010152545

5100RelativeFrequencyPercentFrequencyRating.10(100)=101/20=.05Example:MaradaInnRelativeFrequencyand

PercentBarChartAbarchartisagraphicaldevicefordepictingqualitativedata.Ononeaxis(usuallythehorizontalaxis),wespecifythelabelsthatareusedforeachoftheclasses.Afrequency,relativefrequency,orpercentfrequencyscalecanbeusedfortheotheraxis(usuallytheverticalaxis).Usingabaroffixedwidthdrawnaboveeachclasslabel,weextendtheheightappropriately.Thebarsareseparatedtoemphasizethefactthateachclassisaseparatecategory.BarChartAbarchartisagPoorBelowAverageAverageAboveAverageExcellentFrequencyRatingBarChart12345678910MaradaInnQualityRatingsPoorBelowAverageAboveExcellenParetoDiagramInqualitycontrol,barchartsareusedtoidentifythemostimportantcausesofproblems.Whenthebarsarearrangedindescendingorderofheightfromlefttoright(withthemostfrequentlyoccurringcauseappearingfirst)thebarchartiscalledaParetodiagram.Thisdiagramisnamedforitsfounder,VilfredoPareto,anItalianeconomist.ParetoDiagramInqualitycoPieChartThepiechartisacommonlyusedgraphicaldeviceforpresentingrelativefrequencyandpercent

frequencydistributionsforcategoricaldata.Firstdrawacircle;thenusetherelativefrequenciestosubdividethecircleintosectorsthatcorrespondtotherelativefrequencyforeachclass.Sincethereare360degreesinacircle,aclasswitharelativefrequencyof.25wouldconsume.25(360)=90degreesofthecircle.PieChartThepiechartisa

BelowAverage15%Average25%AboveAverage45%Poor10%Excellent5%

MaradaInn

QualityRatingsPieChartBelowAverageAbovePoorExceInsightsGainedfromthePrecedingPieChartExample:MaradaInnOne-halfofthecustomerssurveyedgaveMaradaaqualityratingof“aboveaverage”or“excellent”(lookingattheleftsideofthepie).Thismightpleasethemanager.Foreachcustomerwhogavean“excellent”rating,thereweretwocustomerswhogavea“poor”rating(lookingatthetopofthepie).Thisshoulddispleasethemanager.InsightsGainedfromthePreceSummarizingQuantitativeDataFrequencyDistributionRelativeFrequencyandPercentFrequencyDistributionsDotPlotHistogramCumulativeDistributionsOgiveSummarizingQuantitativeDataF ThemanagerofHudsonAutowouldliketogainabetterunderstandingofthecostofpartsusedintheenginetune-upsperformedintheshop.Sheexamines50customerinvoicesfortune-ups.Thecostsofparts,roundedtothenearestdollar,arelistedonthenextslide.Example:HudsonAutoRepairFrequencyDistribution ThemanagerofHudsonAutowoSampleofPartsCost($)for50Tune-upsFrequencyDistributionExample:HudsonAutoRepairSampleofPartsCost($)for50FrequencyDistribution2.Determinethewidthofeachclass.3.Determinetheclasslimits.1.Determinethenumberofnon-overlappingclasses.Thethreestepsnecessarytodefinetheclassesforafrequencydistributionwithquantitativedataare:FrequencyDistribution2.DetFrequencyDistributionGuidelinesforDeterminingtheNumberofClassesUsebetween5and20classes.Datasetswithalargernumberofelementsusuallyrequirealargernumberofclasses.Smallerdatasetsusuallyrequirefewerclasses.Thegoalistouseenoughclassestoshowthevariationinthedata,butnotsomanyclassesthatsomecontainonlyafewdataitems.FrequencyDistributionGuidelinFrequencyDistributionGuidelinesforDeterminingtheWidthofEachClassUseclassesofequalwidth.ApproximateClassWidth=Makingtheclassesthesamewidthreducesthechanceofinappropriateinterpretations.FrequencyDistributionGuidelinNoteonNumberofClassesandClassWidthInpractice,thenumberofclassesandtheappropriateclasswidtharedeterminedbytrialanderror.Onceapossiblenumberofclassesischosen,theappropriateclasswidthisfound.Theprocesscanberepeatedforadifferentnumberofclasses.FrequencyDistributionUltimately,theanalystusesjudgmenttodeterminethecombinationofthenumberofclassesandclasswidththatprovidesthebestfrequencydistributionforsummarizingthedata.NoteonNumberofClassesandFrequencyDistributionGuidelinesforDeterminingtheClassLimitsClasslimitsmustbechosensothateachdataitembelongstooneandonlyoneclass.Thelowerclasslimitidentifiesthesmallestpossibledatavalueassignedtotheclass.Theupperclasslimitidentifiesthelargestpossibledatavalueassignedtotheclass.Theappropriatevaluesfortheclasslimitsdependonthelevelofaccuracyofthedata.Anopen-endclassrequiresonlyalowerclasslimitoranupperclasslimit.FrequencyDistributionGuidelinFrequencyDistributionIfwechoosesixclasses:

50-59 60-6970-79 80-89 90-99 100-109

2131677

5Total50PartsCost($)FrequencyApproximateClassWidth=(109-52)/6=9.510Example:HudsonAutoRepairFrequencyDistributionIfwechRelativeFrequencyand

PercentFrequencyDistributions

50-59 60-6970-79 80-89 90-99 100-109PartsCost($)

.04.26.32.14.14

.10Total1.00RelativeFrequency

42632141410100PercentFrequency2/50.04(100)Example:HudsonAutoRepairPercentfrequencyistherelativefrequencymultipliedby100.RelativeFrequencyand

PercentOnly4%ofthepartscostsareinthe$50-59class.Thegreatestpercentage(32%oralmostone-third)ofthepartscostsareinthe$70-79class.30%ofthepartscostsareunder$70.10%ofthepartscostsare$100ormore.InsightsGainedfromthe%FrequencyDistribution:RelativeFrequencyand

PercentFrequencyDistributionsExample:HudsonAutoRepairOnly4%ofthepartscostsaDotPlotOneofthesimplestgraphicalsummariesofdataisadotplot.Ahorizontalaxisshowstherangeofdatavalues.Theneachdatavalueisrepresentedbyadotplacedabovetheaxis.DotPlotOneofthesimplestgrDotPlot50

60

70

80

90

100

110Cost($)Tune-upPartsCostExample:HudsonAutoRepairDotPlot5060HistogramAnothercommongraphicalpresentationofquantitativedataisahistogram.Thevariableofinterestisplacedonthehorizontalaxis.Arectangleisdrawnaboveeachclassintervalwithitsheightcorrespondingtotheinterval’sfrequency,

relativefrequency,orpercentfrequency.Unlikeabargraph,ahistogramhasnonatural

separationbetweenrectanglesofadjacentclasses.HistogramAnothercommongraHistogram24681012141618PartsCost($)Frequency50-5960-6970-79

80-8990-99100-110Tune-upPartsCostExample:HudsonAutoRepairHistogram24681012141618PartsSymmetricHistogramsShowingSkewnessRelativeFrequency.05.10.15.20.25.30.350LefttailisthemirrorimageoftherighttailExamples:heightsandweightsofpeopleSymmetricHistogramsShowingSkHistogramsShowingSkewnessModeratelySkewedLeftRelativeFrequency.05.10.15.20.25.30.350AlongertailtotheleftExample:examscoresHistogramsShowingSkewnessModModeratelyRightSkewedHistogramsShowingSkewnessRel