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A variable isacharacteristicthatvariesfromonepersonorthingto   another.(Example:apersonsage,height,numberofchildren,numberof 0 B cars,eyecolor,favoritetypeofmusic,etc.) ^ p  Typically,avariablecandescribeeitheraquantitativeoraqualitative   characteristicofanindividual.   A quantitative (numerical)variableisavariablethattakesonnumerical DV  values.(Aquantitativevariablehasnaturalunitsofmeasurement.Theunits r ofmeasurementtellushowmuchofsomethingwehaveorhowfaraparttwo  valuesare.)  Ѐ0  Examples:age,height,weight,numberofchildren,numberofcars, *< examscore,distanceonetravelstogettoschool,numberofcoinsina Xj personspocket,etc.(#(# A qualitative (categorical)variableisavariablewhosevaluesaredescriptive,  notnumerical. " 0  Examples:gender,race,eyecolor,favoritetypeofmusic,political l ~ party,birthmonth,handedness(left,right,ambidextrous),school ! district,etc."(#(# Comment#1: $%6" 0  Sometimes,numericallabelsareusedforqualitative(categorical)data. '$  (#(# 0  Example:Whenwecategorizeindividualsbyeyecolor,wemaydenote )&! blueeyesby1,browneyesby2,greeneyesby3,andhazeleyesby4.  +(" (Thiskindofdataissometimescalled codeddata.)Theuseof 8,J)# numericallabelsforcategoricaldatadoesnotmakethedata f-x*$ quantitative. .+%(#(# @(2  0  Whennumericallabelsareusedforqualitative(categorical)data,it J\ willoftenmakenosensetodoarithmetictothedata(forexample, x takinganaverage).(#(# 0  Takeasampleof20adultsandsuppose4ofthemhaveblueeyes,7   havebrowneyes,2havegreeneyes,and7havehazeleyes.Thecoded 0 B datawouldlooklikethis:^ p (#(# @n n 1,1,1,1,2,2,2,2,2,2,2,3,3,4,4,4,4,4,4,4   0  Wecanaveragethesenumbersandget52/20=2.6,butthisresulthas (  nomeaningfulinterpretation.DV (#(# 0  Remember,datahascontext.Ifyouareaskedtoanalyzesomedata,  makesureyouaregiventhecontext!ask Whatdothenumbersinthe  datasetrepresent?Whenwerealizethecontextofthenumbers  aboveiseyecolor,thenweunderstandthattakinganaverageofthose *< numbersisntmeaningful.(Anotherexample:areacodes.)Xj(#(# Comment#2:  0  Somevariablescanbeconsideredquantitative(numerical)or " qualitative(categorical),dependingonwhyyouarelookingatit.>P(#(# 0  Example:_Amazon.com_Ԁisconstantlymonitoringandevolvingtheirweb ! sitetobestservetheircustomersandmaximizetheirsales " performance.Tomakechangestothesite,theyexperiment,collecting #! dataandanalyzingwhatworksbest.SupposeAmazonasksforyour $%6" ageinyears.Thatseemsquantitative,andwouldbeiftheywantto R&d# knowtheaverageageofthosecustomerswhovisittheirsiteafter '$ 3am.ButsupposetheywanttodecidewhichCDtoofferyouina (%  specialdeal.Thenthinkingofyourageinoneofthecategorieschild, )&! teen,adult,orseniormightbemoreuseful. +("(#(# 0  Ifitisntclearwhetheravariableiscategoricalorquantitative,think f-x*$ aboutwhyyouarelookingatitandwhatyouwantittotellyou. .+%(#(# @(3  Comment#3: J\ 0  Atypicalcourseevaluationsurveyasks, Howvaluabledoyouthinkthis  coursewillbetoyou?1=worthless;2=slightly;3=middling;4=  reasonably;5=invaluable.Isthevariableeducationalvaluecategorical   orquantitative?Itdependsonwhatwewantittotellus.0 B(#(# 0  Ateachermightjustcountthenumberofstudentswhogaveeach   responseforhercourse,treatingeducationalvalueasacategorical   variable. (#(# 0  Whentheteacherwantstoseewhetherthecourseisimproving,for DV  example,shemighttreatthestudentresponsesastheamountof r perceivedvalue!ineffect,treatingthevariableasquantitative.But,  whataretheunitsofmeasurement?Thereiscertainlyanorderof  perceivedworth;highernumbersindicatehigherperceivedworth.A  coursethataverages4.5seemsmorevaluablethanonethataverages *< 2,butweshouldbecarefulabouttreatingeducationalvalueaspurely Xj quantitative.Totreatitaspurelyquantitative,wehavetoimagine  thatithas educationalvalueunitsorsomesimilararbitrary  construction.Becausetherearenonaturalunits,weshouldbe  cautious."(#(# 0  Variableslikethisthatreportorderwithoutnaturalunitsareoften l ~ called ordinalvariables .!(#(# Comment#4: #! 0  Somecategoricalvariablesaresimplyidentifiers.Mygradebookhasa R&d# lotofdatainit,includingthingslikestudentID#,major,Test1 '$ score,Test2score,etc.ThevariablestudentID#iscategorical,but (%  thereisexactlyoneindividualineverycategory.Thevariableissimply )&! playingtheroleofanidentifier,andanalyzingitisnotinformative. +("(#(#   8,J)# @(4  So, data isinformationobtainedbyobservingthevaluesofavariable.This J\ istheinformationthatisgatheredinastatisticalstudy.Eachpieceofdata x isanobservationandthesetofallobservationsisthedataset.  1.0  Foreachdescriptionofdata,namethevariablesandspecifyforeach   variablewhetheritsuseindicatesthatitshouldbetreatedas 0 B categoricalorquantitative.^ p (#(# 0  (a)0` (#(#Weighbears.Becauseofthedifficultyofweighingabearinthe   woods,researcherscaughtandmeasured54bears,recording   theirweight,necksize,length,andsex.Theyhopedtofinda (  waytoestimateweightfromtheothermoreeasilydetermined DV  quantities.r` (#` (#   (b)0 ` _Arby_smenu.Alistingpostedbythe_Arby_srestaurantchain l ~ gives,foreachofthesandwichesitsells,thetypeofmeatinthe ! sandwich,thenumberofcalories,andtheservingsizeinounces. " Thedatamightbeusedtoassessthenutritionalvalueofthe #! differentsandwiches.$%6"` (#` (#   R&d# @(5    _(c_)0 ` Babies.Medicalresearchersatalargecityhospitalinvestigating J\ theimpactofprenatalcareonnewbornhealthcollecteddata x from882birthsduring19982000.Theykepttrackofthe  mothersage,thenumberofweeksthepregnancylasted,the  typeofbirth(cesarean,induced,natural),thelevelofprenatal   carethemotherhad(none,minimal,adequate),thebirthweight 0 B andsexofthebaby,andwhetherthebabyexhibitedhealth ^ p  problems(none,minor,major). ` (#` (# QUANTITATIVEDATA:DISCRETEANDCONTINUOUS  Dataconsistingofquantitative(numerical)variablescanbefurtherdivided >P intotwogroups:discreteandcontinuous. l ~ Ifthesetofallpossiblevaluesthevariablemighttakeon,whenpicturedon " thenumberline,consistsonlyofisolatedpoints,thenthenumericaldatais #!  discrete .Therearegapsbetweenconsecutivepossiblevaluesbecause $%6" discretevariablesassumeonlyisolatedvalues. R&d# Ifthesetofallvaluesthevariablemighttakeon,whenpicturedonthe (%  numberline,consistsofanintervalofnumbers(orseveralintervalsof )&! numbers),possiblyunbounded,thenthenumericaldatais continuous .  +(" Notethatdiscretequantitativedatainvolvescounting.Continuous f-x*$ quantitativedatainvolvesmeasurement.  .+% @(6  Example J\ Supposethefiredepartmentmandatesthatallfirefightersmustweigh  between150and250pounds.Theweightofafirefighterwouldbean  exampleofacontinuousvariable,sinceafirefightersweightcouldtakeon   anyvaluebetween150and250pounds. 0 B Supposeweflipacoinandcountthenumberofheads.Thenumberofheads   couldbeanyintegervaluegreaterthanorequalto0.However,itcouldnot   beanynumbergreaterthanorequalto0.Wecouldnot,forexample,get   2.5heads.Therefore,thenumberofheadsmustbeadiscretevariable. (  2.0  Circle discreteor continuousforthevariablesdescribedbelow. r Rememberthatdiscretevariablesarisefromcounting,andcontinuous  variablesarisefrommeasurement.(#(# 0  (a)0` (#(#Thenumberofheadsobtainedwhentwocoinsaretossed *< together.Xj` (#` (# 0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement)  0  (b)0` (#(#Thetotalscoreobtainedwhentwodicearethrown."` (#` (#    `     h      p      x  0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement) l ~ 0  _(c_)0` (#(#Theweightsofyear7pupilsatanearbyschool"` (#` (# 0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement) $%6" 0  (d)0` (#(#Thetimeittakesyoutogettoschooleachday'$` (#` (# 0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement) )&!   8,J)# @(7  0  (e)0` (#(#ThenumberoftouchdownsscoredbytheJonesborohighschool J\ footballteamlastseasonx` (#` (# 0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement)  0  (f)0` (#(#TheheightsofBritishbasketballplayersaged20orover.0 B` (#` (# 0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement)   0  (g)0` (#(#Thetimeittakestorun100meters. ` (#` (# 0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement) DV  0  (h)0` (#(#Thenumberofmatchesinaboxmarked averagecontents50.` (#` (# 0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement)  0  (_i_)0` (#(#Correctanswersoutof10questionsonamentalarithmetictestXj` (#` (# 0   @(#(#Discrete(arisefromcounting)orContinuous(arisefrommeasurement)