商務(wù)統(tǒng)計(jì)學(xué)（第7版）英文 課件全套 戴維·萊文 1 Defining and Collecting Data-13 Multiple Regression

GettingStartedChapterGSObjectivesInthischapteryoulearn:

Thatthepreponderanceofdatamakeslearningaboutstatisticscriticallyimportant.Statisticsisawayofthinkingthatcanleadtobetterdecisions.HowapplyingtheDCOVAframeworkforapplyingstatisticscanhelpsolvebusinessproblems.Thesignificanceofbusinessanalytics.Theopportunitybusinessanalyticsrepresentforbusinessstudents.HowtoprepareforusingMicrosoftExcel?orMinitabwiththisbook.InToday’sBusinessWorldYouCannotEscapeFromDataIntoday’sdigitalworldeverincreasingamountsofdataaregathered,stored,reportedon,andavailableforfurtherstudy.Youheartheworddataeverywhere.Dataarefactsabouttheworldandareconstantlyreportedasnumbersbyaneverincreasingnumberofsources.EachBusinessPersonFacesAChoiceOfHowToDealWithThisExplosionOfDataTheycanignoreitandhopeforthebest.Theycancountonotherpeople’ssummariesofdataandhopetheyarecorrect.Theycandeveloptheirowncapabilityandinsightintodatabylearningaboutstatisticsanditsapplicationtobusiness.StatisticsIsEvolvingSoBusinessesCanUseTheVastAmountOfDataAvailableTheemergingfieldofBusinessAnalyticsmakes“extensiveuseof:DataStatisticalandquantitativeanalysisExplanatory&predictivemodelsFactbasedmanagementtodrivedecisionsandactions.”ToProperlyApplyStatisticsYouShouldFollowAFrameworkToMinimizePossibleErrorsInthisbookwewilluseDCOVADefinethedatayouwanttostudyinordertosolveaproblemormeetanobjectiveCollectthedatafromappropriatesourcesOrganizethedatacollectedbydevelopingtablesVisualizethedatabydevelopingchartsAnalyzethedatacollectedtoreachconclusionsandpresentresultsUsingTheDCOVAFrameworkHelpsYouToApplyStatisticsTo:Summarize&visualizebusinessdataReachconclusionsfromthosedataMakereliablepredictionsaboutbusinessactivitiesImprovebusinessprocessesDefinitionOfSomeTermsVARIABLEAcharacteristicofanitemorindividual.DATAThesetofindividualvaluesassociatedwithavariable.STATISTICSThemethodsthathelptransformdataintousefulinformationfordecisionmakers.DCOVAAreTheseNumbersUsefulInMakingDecisionsAsurveyof1,179adults18andoverreportedthat54%thoughtthat15secondswasanacceptableonlineadlengthbeforeseeingfreecontent.Asurveyreportedwomenweremorelikelythanmentociteseeingphotosorvideos,sharingwithmanpeopleatone,seeingentertainingorfunnyposts,learningaboutwaystohelpothers,andreceivingsupportfrompeopleinyournetworkasreasonstouseFacebook.AstudyfoundthenumberoftimesaspecificproductwasmentionedincommentsintheTwittersocialmessagingservicecouldbeusedtomakeaccuratepredictionsofsalestrendsforthatproduct.WithoutStatisticsYouCan’tDetermineifthenumbersinthesestudiesareusefulinformationValidateclaimsofpredictabilityorcausalitySeepatternsthatlargeamountsofdatasometimesrevealBusinessAnalytics:TheChangingFaceOfStatisticsUsestatisticalmethodstoanalyzeandexploredatatouncoverunforeseenrelationships.Usemanagementsciencemethodstodevelopoptimizationmodelsthatimpactanorganization’sstrategy,planning,andoperations.Useinformationsystems’methodstocollectandprocessdatasetsofallsizes,includingverylargedatasetsthatwouldotherwisebehardtoexamineefficiently.BusinessAnalyticsHasAlreadyBeenAppliedInManyBusinessDecision-MakingContextsHumanresourcemanagers(HR)understandingrelationshipsbetweenHRdrivers,keybusinessoutcomes,employeeskills,capabilities,andmotivation.Financialanalystsdeterminingwhycertaintrendsoccurtopredictfuturefinancialenvironments.Marketersdrivingloyaltyprogramsandcustomermarketingdecisionstodrivesales.Supplychainmanagersplanningandforecastingbasedonproductdistributionandoptimizingsalesdistributionbasedonkeyinventorymeasures.TheGrowthOf“BigData”SpursTheUseOfBusinessAnalytics“BigData”isstillafuzzyconcept.Verylargedatasetsarearisingbecauseoftheautomaticcollectionofhighvolumesofdataatveryfastrates.Attributesthatdistinguish“BigData”fromwellstructuredlargedatasetsare“volume”ofdata,“velocity”ofthedatacollection,and“variety”ofthedata.Statistics:AnImportantPartofYourBusinessEducationYouneedanalyticalskillsfortheincreasinglydata-drivenenvironmentofbusiness.Studiesshowanincreaseinproductivity,innovation,andcompetitivenessfororganizationsthatembracebusinessanalytics.ToquoteHalVarian,thechiefeconomistatGoogleInc.,“thesexyjobinthenext10yearswillbestatisticians.AndI’mnotkidding.”HowToUseThisBookTheUsingStatisticsscenarioatthebeginningandendofeachchapterprovideArealbusinesssituationthatthechapter’stopicscanhelpaddressContextwhichisanimportantpartofthelearningprocessThroughouteachchapteryouwillfindExcel?andMinitabsolutionstoexampleproblems.NumerouscasestudiesareprovidedsoyoucanApplywhatyouhavelearnedEnhanceyouranalytical&communicationskillsSoftwareandStatisticsSoftwareisusedinstatisticstoassistyouinapplyingstatisticalmethods.Thisbookcoverstheuseoftwosoftwarepackages:MicrosoftExcel?--MicrosoftOffice’sdataanalysisapplicationMinitab--adedicatedstatisticalanalysispackage.EitherExcel?orMinitabcanbeusedtolearnandpracticethestatisticalmethodsinthisbook.ChecklistForPreparingtoUseExcel?orMinitabWithThisBook?ReadAppendixCtolearnabouttheonlineresourcesyouneedtomakebestuseofthisbook.?Downloadtheonlineresourcesthatyouwillneedtousethisbook,usingtheinstructionsinAppendixC.?Checkforandapplyupdatestotheprogramthatyouplantouse.(SeetheAppendixSectionD.1instructions).?IfyouplantousePHStat,theVisualExplorationsadd-inworkbooks,ortheAnalysisToolPakwithMicrosoftWindowsExcel,readthespecialinstructionsinAppendixD.?ReadAppendixGtolearnanswerstofrequentlyaskedquestions(FAQs).ChapterSummaryInthischapterwehaveseen:

Thatthepreponderanceofdatathatexistsintheworldmakeslearningaboutstatisticscriticallyimportant.Thatstatisticsisawayofthinkingthatcanleadtobetterdecisions.HowapplyingtheDCOVAframeworkforapplyingstatisticscanhelpyousolvebusinessproblems.Thesignificanceofbusinessanalytics.Theopportunitybusinessanalyticsrepresentsforbusinessstudents.HowtoprepareforusingMicrosoftExcel?orMinitabwiththisbook.DefiningandCollectingDataChapter1ObjectivesInthischapteryoulearn:

Tounderstandissuesthatarisewhendefiningvariables.HowtodefinevariablesHowtocollectdataToidentifydifferentwaystocollectasampleUnderstandthetypesofsurveyerrorsClassifyingVariablesByTypeCategorical(qualitative)variablestakecategoriesastheirvaluessuchas“yes”,“no”,or“blue”,“brown”,“green”.Numerical(quantitative)variableshavevaluesthatrepresentacountedormeasuredquantity.DiscretevariablesarisefromacountingprocessContinuousvariablesarisefromameasuringprocessDCOVAExamplesofTypesofVariablesDCOVAQuestionResponsesVariableTypeDoyouhaveaFacebookprofile?YesorNoCategorical(Qualitative)Howmanytextmessageshaveyousentinthepastthreedays?Numerical(discrete)Howlongdidthemobileappupdatetaketodownload?Numerical(continuous)TypesofVariablesVariablesCategoricalNumerical

DiscreteContinuousExamples:MaritalStatusPoliticalPartyEyeColor

(Definedcategories)Examples:NumberofChildrenDefectsperhour

(Counteditems)Examples:WeightVoltage

(Measuredcharacteristics)DCOVACollectingDataCorrectlyIsACriticalTaskNeedtoavoiddataflawedbybiases,ambiguities,orothertypesoferrors.Resultsfromflaweddatawillbesuspectorinerror.Eventhemostsophisticatedstatisticalmethodsarenotveryusefulwhenthedataisflawed.DCOVADevelopingOperationalDefinitionsIsCrucialToAvoidConfusion/ErrorsAnoperationaldefinitionisaclearandprecisestatementthatprovidesacommonunderstandingofmeaningIntheabsenceofanoperationaldefinitionmiscommunicationsanderrorsarelikelytooccur.Arrivingatoperationaldefinition(s)isakeypartoftheDefinestepofDCOVADCOVAEstablishingABusinessObjectiveFocusesDataCollectionExamplesOfBusinessObjectives:Amarketingresearchanalystneedstoassesstheeffectivenessofanewtelevisionadvertisement.Apharmaceuticalmanufacturerneedstodeterminewhetheranewdrugismoreeffectivethanthosecurrentlyinuse.Anoperationsmanagerwantstomonitoramanufacturingprocesstofindoutwhetherthequalityoftheproductbeingmanufacturedisconformingtocompanystandards.Anauditorwantstoreviewthefinancialtransactionsofacompanyinordertodeterminewhetherthecompanyisincompliancewithgenerallyacceptedaccountingprinciples.DCOVASourcesofDataPrimarySources:ThedatacollectoristheoneusingthedataforanalysisDatafromapoliticalsurveyDatacollectedfromanexperimentObserveddataSecondarySources:ThepersonperformingdataanalysisisnotthedatacollectorAnalyzingcensusdataExaminingdatafromprintjournalsordatapublishedontheinternet.DCOVASourcesofdatafallintofivecategoriesDatadistributedbyanorganizationoranindividualTheoutcomesofadesignedexperimentTheresponsesfromasurveyTheresultsofconductinganobservationalstudyDatacollectedbyongoingbusinessactivitiesDCOVAExamplesOfDataDistributedByOrganizationsorIndividualsFinancialdataonacompanyprovidedbyinvestmentservices.Industryormarketdatafrommarketresearchfirmsandtradeassociations.Stockprices,weatherconditions,andsportsstatisticsindailynewspapers.DCOVAExamplesofDataFromADesignedExperimentConsumertestingofdifferentversionsofaproducttohelpdeterminewhichproductshouldbepursuedfurther.Materialtestingtodeterminewhichsupplier’smaterialshouldbeusedinaproduct.Markettestingonalternativeproductpromotionstodeterminewhichpromotiontousemorebroadly.DCOVAExamplesofSurveyDataAsurveyaskingpeoplewhichlaundrydetergenthasthebeststain-removingabilitiesPoliticalpollsofregisteredvotersduringpoliticalcampaigns.Peoplebeingsurveyedtodeterminetheirsatisfactionwitharecentproductorserviceexperience.DCOVAExamplesofDataCollectedFromObservationalStudiesMarketresearchersutilizingfocusgroupstoelicitunstructuredresponsestoopen-endedquestions.Measuringthetimeittakesforcustomerstobeservedinafastfoodestablishment.Measuringthevolumeoftrafficthroughanintersectiontodetermineifsomeformofadvertisingattheintersectionisjustified.DCOVAExamplesofDataCollectedFromOngoingBusinessActivitiesAbankstudiesyearsoffinancialtransactionstohelpthemidentifypatternsoffraud.EconomistsutilizedataonsearchesdoneviaGoogletohelpforecastfutureeconomicconditions.Marketingcompaniesusetrackingdatatoevaluatetheeffectivenessofawebsite.DCOVADataIsCollectedFromEitherAPopulationorASamplePOPULATIONApopulationconsistsofalltheitemsorindividualsaboutwhichyouwanttodrawaconclusion.Thepopulationisthe“l(fā)argegroup”SAMPLEAsampleistheportionofapopulationselectedforanalysis.Thesampleisthe“smallgroup”DCOVAPopulationvs.SamplePopulationSampleAlltheitemsorindividualsaboutwhichyouwanttodrawconclusion(s)AportionofthepopulationofitemsorindividualsDCOVACollectingDataViaSamplingIsUsedWhenSelectingASampleIsLesstimeconsumingthanselectingeveryiteminthepopulation.Lesscostlythanselectingeveryiteminthepopulation.Lesscumbersomeandmorepracticalthananalyzingtheentirepopulation.DCOVAThingsToConsider/DealWithInPotentialSourcesOfDataIsthesourceofdatastructuredorunstructured?Howiselectronicdataformatted?Howisdataencoded?DCOVAStructuredDataFollowsAnOrganizingPrinciple&UnstructuredDataDoesNotAStockTickerProvidesStructuredData:Thestocktickerrepeatedlyreportsacompanyname,thenumberofshareslasttraded,thebidprice,andthepercentchangeinthestockprice.Duetotheirinherentstructure,datafromtablesandformsarestructureddata.E-mailsfromfivepeopleconcerningstocktradesisanexampleofunstructureddata.Inthesee-mailsyoucannotcountontheinformationbeingsharedinaspecificorderorformat.ThisbookdealsexclusivelywithstructureddataDCOVAAllOfTheMethodsInThisBookDealWithStructuredDataTousethetechniquesinthisbookonunstructureddatayouneedtoconverttheunstructuredintostructureddata.Formanyofthequestionsyoumightwanttoanswer,thestartingpointcan/willbetabulardata.DCOVADataCanBeFormattedand/orEncodedInMoreThanOneWaySomeelectronicformatsaremorereadilyusablethanothers.Differentencodingscanimpacttheprecisionofnumericalvariablesandcanalsoimpactdatacompatibility.Asyouidentifyandchoosesourcesofdatayouneedtoconsider/dealwiththeseissuesDCOVADataCleaningIsOftenANecessaryActivityWhenCollectingDataOftenfind“irregularities”inthedataTypographicalordataentryerrorsValuesthatareimpossibleorundefinedMissingvaluesOutliersWhenfoundtheseirregularitiesshouldbereviewed/addressedBothExcel&MinitabcanbeusedtoaddressirregularitiesDCOVAAfterCollectionItIsOftenHelpfulToRecodeSomeVariablesRecodingavariablecaneithersupplementorreplacetheoriginalvariable.Recodingacategoricalvariableinvolvesredefiningcategories.Recodingaquantitativevariableinvolveschangingthisvariableintoacategoricalvariable.Whenrecodingbesurethatthenewcategoriesaremutuallyexclusive(categoriesdonotoverlap)andcollectivelyexhaustive(categoriescoverallpossiblevalues).DCOVAASamplingProcessBeginsWithASamplingFrameThesamplingframeisalistingofitemsthatmakeupthepopulationFramesaredatasourcessuchaspopulationlists,directories,ormapsInaccurateorbiasedresultscanresultifaframeexcludescertainportionsofthepopulationUsingdifferentframestogeneratedatacanleadtodissimilarconclusionsDCOVATypesofSamplesSamplesNon-ProbabilitySamplesJudgmentProbabilitySamplesSimpleRandomSystematicStratifiedClusterConvenienceDCOVATypesofSamples:

NonprobabilitySampleInanonprobabilitysample,itemsincludedarechosenwithoutregardtotheirprobabilityofoccurrence.Inconveniencesampling,itemsareselectedbasedonlyonthefactthattheyareeasy,inexpensive,orconvenienttosample.Inajudgmentsample,yougettheopinionsofpre-selectedexpertsinthesubjectmatter.

DCOVATypesofSamples:

ProbabilitySampleInaprobabilitysample,itemsinthesamplearechosenonthebasisofknownprobabilities.ProbabilitySamplesSimple

RandomSystematicStratifiedClusterDCOVAProbabilitySample:

SimpleRandomSampleEveryindividualoritemfromtheframehasanequalchanceofbeingselectedSelectionmaybewithreplacement(selectedindividualisreturnedtoframeforpossiblereselection)orwithoutreplacement(selectedindividualisn’treturnedtotheframe).Samplesobtainedfromtableofrandomnumbersorcomputerrandomnumbergenerators.DCOVASelectingaSimpleRandomSampleUsingARandomNumberTableSamplingFrameForPopulationWith850ItemsItemNameItem#BevR. 001UlanX. 002. .. .. .. .JoannP. 849PaulF. 850PortionOfARandomNumberTable492808892435779002838116307275111000234012860746979664489439098932399720048494208887208401TheFirst5ItemsinasimplerandomsampleItem#492Item#808Item#892--doesnotexistsoignoreItem#435Item#779Item#002DCOVADecideonsamplesize:nDivideframeofNindividualsintogroupsofkindividuals:k=N/nRandomlyselectoneindividualfromthe1stgroupSelecteverykthindividualthereafterProbabilitySample:

SystematicSampleN=40n=4k=10FirstGroupDCOVAProbabilitySample:

StratifiedSampleDividepopulationintotwoormoresubgroups(calledstrata)accordingtosomecommoncharacteristicAsimplerandomsampleisselectedfromeachsubgroup,withsamplesizesproportionaltostratasizesSamplesfromsubgroupsarecombinedintooneThisisacommontechniquewhensamplingpopulationofvoters,stratifyingacrossracialorsocio-economiclines.PopulationDividedinto4strataDCOVAProbabilitySample

ClusterSamplePopulationisdividedintoseveral“clusters,”eachrepresentativeofthepopulationAsimplerandomsampleofclustersisselectedAllitemsintheselectedclusterscanbeused,oritemscanbechosenfromaclusterusinganotherprobabilitysamplingtechniqueAcommonapplicationofclustersamplinginvolveselectionexitpolls,wherecertainelectiondistrictsareselectedandsampled.Populationdividedinto16clusters.RandomlyselectedclustersforsampleDCOVAProbabilitySample:

ComparingSamplingMethodsSimplerandomsampleandSystematicsampleSimpletouseMaynotbeagoodrepresentationofthepopulation’sunderlyingcharacteristicsStratifiedsampleEnsuresrepresentationofindividualsacrosstheentirepopulationClustersampleMorecosteffectiveLessefficient(needlargersampletoacquirethesamelevelofprecision)DCOVAEvaluatingSurveyWorthinessWhatisthepurposeofthesurvey?Isthesurveybasedonaprobabilitysample?Coverageerror–appropriateframe?Nonresponseerror–followupMeasurementerror–goodquestionselicitgoodresponsesSamplingerror–alwaysexistsDCOVATypesofSurveyErrorsCoverageerrororselectionbiasExistsifsomegroupsareexcludedfromtheframeandhavenochanceofbeingselectedNonresponseerrororbiasPeoplewhodonotrespondmaybedifferentfromthosewhodorespondSamplingerrorVariationfromsampletosamplewillalwaysexistMeasurementerrorDuetoweaknessesinquestiondesignand/orrespondenterrorDCOVATypesofSurveyErrorsCoverageerrorNonresponseerrorSamplingerrorMeasurementerrorExcludedfromframeFollowuponnonresponsesRandomdifferencesfromsampletosampleBadorleadingquestion(continued)DCOVAChapterSummaryInthischapterwehavediscussed:

ThetypesofvariablesusedinstatisticsHowtocollectdataThedifferentwaystocollectasampleThetypesofsurveyerrorsOrganizingandVisualizingVariablesChapter2ObjectivesInthischapteryoulearn:

Methodstoorganizevariables.Methodstovisualizevariables.Methodstoorganizeorvisualizemorethanonevariableatthesametime.Principlesofpropervisualizations.CategoricalDataAreOrganizedByUtilizingTablesDCOVACategoricalDataTallyingData

SummaryTable

OneCategoricalVariable

TwoCategoricalVariablesContingencyTableOrganizingCategoricalData:SummaryTableAsummarytabletalliesthefrequenciesorpercentagesofitemsinasetofcategoriessothatyoucanseedifferencesbetweencategories.

ReasonForShoppingOnline?PercentBetterPrices37%Avoidingholidaycrowdsorhassles29%Convenience18%Betterselection13%Shipsdirectly3%DCOVAMainReasonYoungAdultsShopOnlineSource:Dataextractedandadaptedfrom“MainReasonYoungAdultsShopOnline?”USAToday,December5,2012,p.1A.AContingencyTableHelpsOrganizeTwoorMoreCategoricalVariablesUsedtostudypatternsthatmayexistbetweentheresponsesoftwoormorecategoricalvariablesCrosstabulatesortalliesjointlytheresponsesofthecategoricalvariablesFortwovariablesthetalliesforonevariablearelocatedintherowsandthetalliesforthesecondvariablearelocatedinthecolumnsDCOVAContingencyTable-ExampleArandomsampleof400invoicesisdrawn.Eachinvoiceiscategorizedasasmall,medium,orlargeamount.Eachinvoiceisalsoexaminedtoidentifyifthereareanyerrors.Thisdataarethenorganizedinthecontingencytabletotheright.DCOVANoErrorsErrorsTotalSmallAmount17020190MediumAmount10040140LargeAmount65570Total33565400ContingencyTableShowingFrequencyofInvoicesCategorizedBySizeandThePresenceOfErrorsContingencyTableBasedOnPercentageOfOverallTotalNoErrorsErrorsTotalSmallAmount17020190MediumAmount10040140LargeAmount65570Total33565400DCOVANoErrorsErrorsTotalSmallAmount42.50%5.00%47.50%MediumAmount25.00%10.00%35.00%LargeAmount16.25%1.25%17.50%Total83.75%16.25%100.0%42.50%=170/40025.00%=100/40016.25%=65/40083.75%ofsampledinvoiceshavenoerrorsand47.50%ofsampledinvoicesareforsmallamounts.ContingencyTableBasedOnPercentageofRowTotalsNoErrorsErrorsTotalSmallAmount17020190MediumAmount10040140LargeAmount65570Total33565400DCOVANoErrorsErrorsTotalSmallAmount89.47%10.53%100.0%MediumAmount71.43%28.57%100.0%LargeAmount92.86%7.14%100.0%Total83.75%16.25%100.0%89.47%=170/19071.43%=100/14092.86%=65/70Mediuminvoiceshavealargerchance(28.57%)ofhavingerrorsthansmall(10.53%)orlarge(7.14%)invoices.ContingencyTableBasedOnPercentageOfColumnTotalsNoErrorsErrorsTotalSmallAmount17020190MediumAmount10040140LargeAmount65570Total33565400DCOVANoErrorsErrorsTotalSmallAmount50.75%30.77%47.50%MediumAmount29.85%61.54%35.00%LargeAmount19.40%7.69%17.50%Total100.0%100.0%100.0%50.75%=170/33530.77%=20/65Thereisa61.54%chancethatinvoiceswitherrorsareofmediumsize.TablesUsedForOrganizing

NumericalDataDCOVANumericalDataOrderedArrayCumulativeDistributionsFrequencyDistributionsOrganizingNumericalData:

OrderedArrayAnorderedarrayisasequenceofdata,inrankorder,fromthesmallestvaluetothelargestvalue.Showsrange(minimumvaluetomaximumvalue)Mayhelpidentifyoutliers(unusualobservations)AgeofSurveyedCollegeStudentsDayStudents161717181818191920202122222527323842NightStudents181819192021232832334145DCOVAOrganizingNumericalData:

FrequencyDistributionThefrequencydistributionisasummarytableinwhichthedataarearrangedintonumericallyorderedclasses.

Youmustgiveattentiontoselectingtheappropriatenumberofclassgroupingsforthetable,determiningasuitablewidthofaclassgrouping,andestablishingtheboundariesofeachclassgroupingtoavoidoverlapping.Thenumberofclassesdependsonthenumberofvaluesinthedata.Withalargernumberofvalues,typicallytherearemoreclasses.Ingeneral,afrequencydistributionshouldhaveatleast5butnomorethan15classes.Todeterminethewidthofaclassinterval,youdividetherange(Highestvalue–Lowestvalue)ofthedatabythenumberofclassgroupingsdesired.DCOVAOrganizingNumericalData:

FrequencyDistributionExampleExample:Amanufacturerofinsulationrandomlyselects20winterdaysandrecordsthedailyhightemperature24,35,17,21,24,37,26,46,58,30,32,13,12,38,41,43,44,27,53,27DCOVAOrganizingNumericalData:

FrequencyDistributionExampleSortrawdatainascendingorder:

12,13,17,21,24,24,26,27,27,30,32,35,37,38,41,43,44,46,53,58Findrange:58-12=46Selectnumberofclasses:5(usuallybetween5and15)Computeclassinterval(width):10(46/5thenroundup)Determineclassboundaries(limits):Class1:10butlessthan20Class2:20butlessthan30Class3:30butlessthan40Class4:40butlessthan50Class5:50butlessthan60Computeclassmidpoints:15,25,35,45,55Countobservations&assigntoclassesDCOVAOrganizingNumericalData:FrequencyDistributionExample

ClassMidpoints Frequency10butlessthan2015 320butlessthan3025 630butlessthan4035 540butlessthan5045 450butlessthan6055 2

Total

20Datainorderedarray:12,13,17,21,24,24,26,27,27,30,32,35,37,38,41,43,44,46,53,58DCOVAOrganizingNumericalData:Relative&PercentFrequencyDistributionExample

ClassFrequency10butlessthan203.1515%20butlessthan306.3030%30butlessthan405.2525%40butlessthan504.2020%50butlessthan602.1010%

Total

201.00100%RelativeFrequency

PercentageDCOVARelativeFrequency=Frequency/Total,e.g.0.10=2/20OrganizingNumericalData:CumulativeFrequencyDistributionExampleClass10butlessthan20 315%315%20butlessthan30 630%945%30butlessthan40 525%1470%40butlessthan50 420%1890%50butlessthan60 210%20100%Total 20100 20 100%

PercentageCumulativePercentageCumulativePercentage=CumulativeFrequency/Total*100e.g.45%=100*9/20FrequencyCumulativeFrequencyDCOVAWhyUseaFrequencyDistribution?ItcondensestherawdataintoamoreusefulformItallowsforaquickvisualinterpretationofthedataItenablesthedeterminationofthemajorcharacteristicsofthedatasetincludingwherethedataareconcentrated/clusteredDCOVAFrequencyDistribut