统计学英文版

Part1GatheringandExploringData(descriptivestatistics)DifferentTypesofData(2.1)VariableAvariableisanycharacteristicobservedonthesubjectsinastudy.Examples:Maritalstatus,Height,Weight,IQ,Sqft,Price,NE.AvariablecanbeclassifiedaseitherCategorical(inCategories),orQuantitative(Numerical)Avariablecanbeclassifiedascategoricalifeachobservationbelongstooneofasetofcategories:Examples:Gender(MaleorFemale)ReligiousAffiliation(Catholic,Jewish,…)TypeofResidence(Apartment,Condo,…)BeliefinLifeAfterDeath(YesorNo)NE(Locatedinnortheastsectorofcity(1)ornot(0))Avariableiscalledquantitativeifobservationsonittakenumericalvaluesthatrepresentdifferentmagnitudesofthevariable.Examples:Age,NumberofSiblings,AnnualIncome,Sellingprice,SqftDiscreteversuscontinuousquantitativevariables
Aquantitativevariableisdiscreteifitspossiblevaluesformasetofseparatenumbers,suchas0,1,2,3,…
ThesetofpossiblevaluesisnotdenseExamples:oNumberofpetsinahouseholdoNumberofchildreninafamilyoNumberofforeignlanguagesspokenbyanindividual
Aquantitativevariableiscontinuousifitspossiblevaluesformaninterval
ThesetofpossiblevaluesisdenseExamples:oHeight/WeightoAgeoBloodpressureExerciseIdentifythevariabletype1.Numberofsiblingsinafamily2.Countyofresidence3.Distance(inmiles)ofcommutetoschool4.Maritalstatus5.Lengthoftimetotakeatest6.Numberofpeoplewaitinginline7.Numberofspeedingticketsreceivedlastyear8.Yourdog’sweightProportion&Percentage(RelativeFrequencies)Theproportionoftheobservationsthatfallinacertaincategoryisthefrequency(count)ofobservationsinthatcategorydividedbythetotalnumberofobservationsFrequencyofthatcategorySumofallfrequenciesThepercentageistheproportionmultipliedby100ProportionsandpercentagesarealsocalledrelativefrequenciesExampleTableclassifiesthe630parliamentaryseatsoftheItalianchamberofdeputiesbycoalition(2013elections).CoalitionSeatsFreq.Prop.Perc.PierluigiBersani3450.54854.8SilvioBerlusconi1250.19819.8BeppeGrillo1090.17317.3MarioMonti470.0757.46Valleed'Aoste10.0020.16MAIAE20.0030.32USEI10.0020.16AntonioIngroia000Total6301100so,forGrillo,345isthefrequency.0.548=345/630istheproportionandrelativefrequency.54.8isthepercentage0.548×100=54.8%.FrequencyTableAfrequencytableisalistingofpossiblevaluesforavariable,togetherwiththenumberofobservationsand/orrelativefrequenciesforeachvalue.RawdataFrequencytableCodeGenderGendernifipi000001FF10000.011000002MM990000.9999......1000001.00100100000FExampleAstockbrokerhasbeenfollowingdifferentstocksoverthelastmonthandhasrecordedwhetherastockisup,thesame,ordowninvalue.Theresultswere:•Whatarethesubjects?•Whatisthevariableofinterest?•Whattypeofvariableisit?•Addproportionstothisfrequencytable.1.PerformanceofstockUpSameDownCount21712Describedatausinggraphicalsummaries(2.2)Distribution
Agraphorfrequencytabledescribesadistribution.
Adistributiontellsusthepossiblevalues/categoriesavariabletakesaswellastheoccurrenceofthosevalues(frequencyorrelativefrequencyorpercentage)Inthe2008GeneralSocialSurvey,2020respondentsansweredthequestion,Howmanychildrenhaveyoueverhad?TheresultswereGraphsforcategoricaldata:bargraphsandpiechartsUsepiechartsandbargraphstosummarizecategoricalvariables:
PieChart.oAcirclewhereeachcategoryisrepresentedasa“sliceofthepie”oThesizeofeachpiesliceisproportionaltothepercentageofobservationsfallinginthatcategory
BarGraph.oBarGraphsdisplayaverticalbarforeachcategoryoTheheightofeachbarrepresentseithercounts(“frequencies”)orpercentages(“relativefrequencies”)forthatcategoryPieChartCARCOMPANIESnipiFIAT3803052FORD1282018OPEL1272017RENAULT963013TOTALI7320010052%13%17%18%FIATRENAULTOPELFORD52%18%17%13%CarssoldFIATFORDOPELRENAULTBarGraphCountsPercentages(I=Italy,F=France)Piechart:easiertocompareonecategorywiththewholeBargraph:easiertocomparecategoriesBargraphsarecalledParetoChartswhenthecategoriesareorderedbytheirfrequency,fromthetallestbartotheshortestbarRENAULTOPELFORDFIATVendite403020100RENAULTOPELFORDFIAT706050403020100FIGraphsforquantitativedata:dotplotShowsadotforeachsubject(observation)placedaboveitsvalueonanumberline.Toconstructadotplot•Drawahorizontallineandlabelitwiththenameofthevariable.•Markregularvaluesofthevariableonit.•Foreachobservation,placeadotaboveitsvalueonthenumberline.Graphsforquantitativedata:histogramsAHistogramisagraphthatusesbarstoportraythefrequenciesortherelativefrequenciesofthepossibleoutcomesforaquantitativevariableStepsforconstructingahistogram1.Dividetherangeofthedataintointervalsofequalwidth2.Countthenumberofobservationsineachinterval,creatingafrequencytable3.Onthehorizontalaxis,labelthevaluesortheendpointsoftheintervals.4.Drawabarovereachvalueorintervalwithheightequaltoitsfrequency(orproportionorpercentage),valuesofwhicharemarkedontheverticalaxis.5.LabelandtitleappropriatelySodiumData:021026012522029021014022020012517025015017070230200290180DisplayingDataoverTime:timeplots
Usedfordisplayingatimeseries,adatasetcollectedovertime.
Plotseachobservationontheverticalscaleagainstthetimeitwasmeasuredonthehorizontalscale.Pointsareusuallyconnected.
Commonpatternsinthedataovertime,knownastrends,shouldbenoted.Meas