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Chapter1

DataandStatisticsDataDataSourcesDescriptiveStatisticsStatisticalInferenceComputersandStatisticalAnalysisDataMiningEthicalGuidelinesforStatisticalPracticeApplicationsinBusinessandEconomicsStatisticsStatisticsThetermstatisticscanrefertonumericalfactssuchasaverages,medians,percents,andindexnumbersthathelpusunderstandavarietyofbusinessandeconomicsituations.Statisticscanalsorefertotheartandscienceofcollecting,analyzing,presenting,andinterpretingdata.Applicationsin

BusinessandEconomicsAccounting

EconomicsPublicaccountingfirmsusestatisticalsamplingprocedureswhenconductingauditsfortheirclients.Economistsusestatisticalinformationinmakingforecastsaboutthefutureoftheeconomyorsomeaspectofit.Financialadvisorsuseprice-earningsratiosanddividendyieldstoguidetheirinvestmentadvice.FinanceApplicationsin

BusinessandEconomicsAvarietyofstatisticalqualitycontrolchartsareusedtomonitortheoutputofaproductionprocess.

ProductionElectronicpoint-of-salescannersatretailcheckoutcountersareusedtocollectdataforavarietyofmarketingresearchapplications.MarketingDataandDataSets

Dataarethefactsandfigurescollected,analyzed,andsummarizedforpresentationandinterpretation.Allthedatacollectedinaparticularstudyarereferredtoasthedatasetforthestudy.

Elementsaretheentitiesonwhichdataarecollected.Avariableisacharacteristicofinterestfortheelements.Thesetofmeasurementsobtainedforaparticularelementiscalledanobservation.Thetotalnumberofdatavaluesinacompletedatasetisthenumberofelementsmultipliedbythenumberofvariables.Elements,Variables,andObservationsAdatasetwithnelementscontainsnobservations.StockAnnualEarn/ExchangeSales($M)Share($)Data,DataSets,

Elements,Variables,andObservationsCompanyDataram EnergySouthKeystoneLandCarePsychemedicsNQ 73.10 0.86N 74.00 1.67N 365.70 0.86NQ 111.40 0.33N 17.60 0.13VariablesElementNamesDataSetObservationScalesofMeasurementThescaleindicatesthedatasummarizationandstatisticalanalysesthataremostappropriate.Thescaledeterminestheamountofinformationcontainedinthedata.Scalesofmeasurementinclude:NominalOrdinalIntervalRatioScalesofMeasurementNominalAnonnumericlabelornumericcodemaybeused.Dataarelabelsornamesusedtoidentifyanattributeoftheelement.Example:StudentsofauniversityareclassifiedbytheschoolinwhichtheyareenrolledusinganonnumericlabelsuchasBusiness,Humanities,Education,andsoon.Alternatively,anumericcodecouldbeusedfortheschoolvariable(e.g.1denotesBusiness,2denotesHumanities,3denotesEducation,andsoon).ScalesofMeasurementNominalScalesofMeasurementOrdinalAnonnumericlabelornumericcodemaybeused.Thedatahavethepropertiesofnominaldataandtheorderorrankofthedataismeaningful.ScalesofMeasurementOrdinalExample:StudentsofauniversityareclassifiedbytheirclassstandingusinganonnumericlabelsuchasFreshman,Sophomore,Junior,orSenior.Alternatively,anumericcodecouldbeusedfortheclassstandingvariable(e.g.1denotesFreshman,2denotesSophomore,andsoon).ScalesofMeasurementIntervalIntervaldataarealwaysnumeric.Thedatahavethepropertiesofordinaldata,andtheintervalbetweenobservationsisexpressedintermsofafixedunitofmeasure.ScalesofMeasurementIntervalExample:MelissahasanSATscoreof1885,whileKevinhasanSATscoreof1780.Melissascored105pointsmorethanKevin.ScalesofMeasurementRatioThedatahaveallthepropertiesofintervaldataandtheratiooftwovaluesismeaningful.Variablessuchasdistance,height,weight,andtimeusetheratioscale.Thisscalemustcontainazerovaluethatindicatesthatnothingexistsforthevariableatthezeropoint.ScalesofMeasurementRatioExample:Melissa’scollegerecordshows36credithoursearned,whileKevin’srecordshows72credithoursearned.KevinhastwiceasmanycredithoursearnedasMelissa.Datacanbefurtherclassifiedasbeingcategoricalorquantitative.Thestatisticalanalysisthatisappropriatedependsonwhetherthedataforthevariablearecategoricalorquantitative.Ingeneral,therearemorealternativesforstatisticalanalysiswhenthedataarequantitative.CategoricalandQuantitativeDataCategoricalData

LabelsornamesusedtoidentifyanattributeofeachelementOftenreferredtoasqualitativedataUseeitherthenominalorordinalscaleofmeasurementCanbeeithernumericornonnumericAppropriatestatisticalanalysesareratherlimitedQuantitativeDataQuantitativedataindicatehowmanyorhowmuch:

discrete,ifmeasuringhowmany

continuous,ifmeasuringhowmuchQuantitativedataarealwaysnumeric.Ordinaryarithmeticoperationsaremeaningfulforquantitativedata.ScalesofMeasurementCategoricalQuantitativeNumericNumericNon-numericDataNominalOrdinalNominalOrdinalIntervalRatioCross-SectionalData

Cross-sectionaldataarecollectedatthesameorapproximatelythesamepointintime.

Example:datadetailingthenumberofbuildingpermitsissuedinFebruary2010ineachofthecountiesofOhioTimeSeriesData

Timeseriesdataarecollectedoverseveraltimeperiods.

Example:datadetailingthenumberofbuildingpermitsissuedinLucasCounty,Ohioineachofthelast36monthsTimeSeriesDataU.S.AveragePricePerGallonForConventionalRegularGasolineSource:EnergyInformationAdministration,U.S.DepartmentofEnergy,May2009.DataSourcesExistingSources

Internalcompanyrecords–almostanydepartmentBusinessdatabaseservices–DowJones&Co.Governmentagencies-U.S.DepartmentofLaborIndustryassociations–TravelIndustryAssociationofAmericaSpecial-interestorganizations–GraduateManagementAdmissionCouncilInternet–moreandmorefirmsRecordSomeoftheDataAvailableDataSourcesDataAvailableFromInternalCompanyRecords

EmployeerecordsProductionrecordsInventoryrecordsSalesrecordsCreditrecordsCustomerprofilename,address,socialsecuritynumberpartnumber,quantityproduced,directlaborcost,materialcostpartnumber,quantityinstock,reorderlevel,economicorderquantityproductnumber,salesvolume,salesvolumebyregioncustomername,creditlimit,accountsreceivablebalanceage,gender,income,householdsizeGovernmentAgencySomeoftheDataAvailableDataSourcesDataAvailableFromSelectedGovernmentAgenciesCensusBureauFederalReserveBoardOfficeofMgmt.&Budget/ombDepartmentofCommerceBureauofLaborStatisticsPopulationdata,numberofhouseholds,householdincomeDataonmoneysupply,exchangerates,discountratesDataonrevenue,expenditures,debtoffederalgovernmentDataonbusinessactivity,valueofshipments,profitbyindustryCustomerspending,unemploymentrate,hourlyearnings,safetyrecordDataSourcesStatisticalStudies-ExperimentalInexperimentalstudiesthevariableofinterestisfirstidentified.Thenoneormoreothervariablesareidentifiedandcontrolledsothatdatacanbeobtainedabouthowtheyinfluencethevariableofinterest.Thelargestexperimentalstudyeverconductedisbelievedtobethe1954PublicHealthServiceexperimentfortheSalkpoliovaccine.NearlytwomillionU.S.children(grades1-3)wereselected.StatisticalStudies-ObservationalDataSourcesInobservational(nonexperimental)studiesnoattemptismadetocontrolorinfluencethevariablesofinterest.asurveyisagoodexampleStudiesofsmokersandnonsmokersareobservationalstudiesbecauseresearchersdonotdetermineorcontrolwhowillsmokeandwhowillnotsmoke.DataAcquisitionConsiderationsTimeRequirementCostofAcquisitionDataErrorsSearchingforinformationcanbetimeconsuming.Informationmaynolongerbeusefulbythetimeitisavailable.Organizationsoftenchargeforinformationevenwhenitisnottheirprimarybusinessactivity.Usinganydatathathappentobeavailableorwereacquiredwithlittlecarecanleadtomisleadinginformation.DescriptiveStatisticsMostofthestatisticalinformationinnewspapers,magazines,companyreports,andotherpublicationsconsistsofdatathataresummarizedandpresentedinaformthatiseasytounderstand.Suchsummariesofdata,whichmaybetabular,graphical,ornumerical,arereferredtoasdescriptivestatistics.Example:HudsonAutoRepair ThemanagerofHudsonAutowouldliketohaveabetterunderstandingofthecostofpartsusedintheenginetune-upsperformedinhershop.Sheexamines50customerinvoicesfortune-ups.Thecostsofparts,roundedtothenearestdollar,arelistedonthenextslide.Example:HudsonAutoRepairSampleofPartsCost($)for50Tune-upsTabularSummary:

FrequencyandPercentFrequency50-5960-6970-7980-8990-99100-109

2131677

550426321414

10100(2/50)100Parts

Cost($)

FrequencyPercentFrequencyExample:HudsonAutoGraphicalSummary:Histogram24681012141618PartsCost($)Frequency50-5960-6970-79

80-8990-99100-110Tune-upPartsCostExample:HudsonAutoNumericalDescriptiveStatisticsHudson’saveragecostofparts,basedonthe50tune-upsstudied,is$79(foundbysummingthe50costvaluesandthendividingby50).Themostcommonnumericaldescriptivestatisticistheaverage(ormean).Theaveragedemonstratesameasureofthecentraltendency,orcentrallocation,ofthedataforavariable.StatisticalInference

PopulationSampleStatisticalinferenceCensusSamplesurvey-thesetofallelementsofinterestinaparticularstudy-asubsetofthepopulation-theprocessofusingdataobtainedfromasampletomakeestimatesandtesthypothesesaboutthecharacteristicsofapopulation-collectingdatafortheentirepopulation-collectingdataforasampleProcessofStatisticalInference1.Populationconsistsofalltune-ups.Averagecostofpartsisunknown.2.Asampleof50enginetune-upsisexamined.Thesampledataprovideasampleaveragepartscostof$79pertune-up.4.Thesampleaverageisusedtoestimatethepopulationaverage.ComputersandStatisticalAnalysisStatisticiansoftenusecomputersoftwaretoperformthestatisticalcomputationsrequiredwithlargeamountsofdata.Tofacilitatecomputerusage,manyofthedatasetsinthisbookareavailableonthewebsitethataccompaniesthetext.ThedatafilesmaybedownloadedineitherMinitaborExcelformats.Also,theExceladd-inStatToolscanbedownloadedfromthewebsite.Chapterendingappendicescoverthestep-by-stepproceduresforusingMinitab,Excel,andStatTools.DataWarehousingOrganizationsobtainlargeamountsofdataonadailybasisbymeansofmagneticcardreaders,barcodescanners,pointofsaleterminals,andtouchscreenmonitors.Wal-Martcapturesdataon20-30milliontransactionsperday.Visaprocesses6,800paymenttransactionspersecond.Capturing,storing,andmaintainingthedata,referredtoasdatawarehousing,isasignificantundertaking.DataMiningAnalysisofthedatainthewarehousemightaidindecisionsthatwillleadtonewstrategiesandhigherprofitsfortheorganization.Usingacombinationofproceduresfromstatistics,mathematics,andcomputerscience,analysts“mine

thedata”toconvertitintousefulinformation.Themosteffectivedataminingsystemsuseautomatedprocedurestodiscoverrelationshipsinthedataandpredictfutureoutcomes,…promptedbyonlygeneral,evenvague,queriesbytheuser.DataMiningApplicationsThemajorapplicationsofdatamininghavebeenmadebycompanieswithastrongconsumerfocussuchasretail,financial,andcommunicationfirms.Dataminingisusedtoidentifyrelatedproductsthatcustomerswhohavealreadypurchasedaspecificproductarealsolikelytopurchase(andthenpop-upsareusedtodrawattentiontothoserelatedproducts).Asanotherexample,dataminingisusedtoidentifycustomerswhoshouldreceivespecialdiscountoffersbasedontheirpastpurchasingvolumes.DataMiningRequirementsStatisticalmethodologysuchasmultipleregression,logisticregression,andcorrelationareheavilyused.Alsoneededarecomputersciencetechnologiesinvolvingartificialintelligenceandmachinelearning.Asignificantinvestmentintimeandmoneyisrequiredaswell.DataMiningModelReliabilityFindingastatisticalmodelthatworkswellforaparticularsampleofdatadoesnotnecessarilymeanthatitcanbereliablyappliedtootherdata.Withtheenormousamountofdataavailable,the

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