Name______________________________________________ APStatistics UNIT1Date______________________Period_____________ SectionIII:Notes1.2–DisplayingQuantitativeDataI.DisplayingQuantitativeDataWaystoDisplayQuantitativeData:

Dotplots Histograms StemandLeaf Box-and-Whisker(Boxplots)DescribingDisplaysofData:

SymmetricGraph:______________________________________________________________________________________________________________________________________________________________________________________________________.Pictureofadistributionskewedtotheright: Pictureofadistributionskewedtotheleft:

YouMUSThavetheseaddressedwhenyoudescribeadistribution:SUCSThetypesofgraphsabovehelpyoutoidentifytheSUCS Shape

Unusualdata(includingoutliers) Center SpreadofthedistributionThisisthegeneralstrategyforinterpretingquantitativedata.Shape:•Dothe“humps”haveasingle,centralhumporseveralseparatedhumps?Humps=modes Describingshape: Withonepeak:________________________ Withtwopeaks:_______________________ Withthreeormore:________________________ Doesn’tappeartohaveanyobviousmode:_________________________________ •Lookatthemode:Howmanymodes?Bimodal,etc.-giveadescriptionoftheshape •Lookforsymmetry:Isthehistogramsymmetric?Directionoftheskew •Tails:thinnerendofthedistribution.Ifonetailstretchesoutfartherthantheotherendof

thedistribution,itissaidtobeskewed. •Skewedtotheright(___________________________________________________________) •Skewedtotheleft(___________________________________________________________) •ClassificationsofSkewness:StronglySkewed/ModeratelySkewed/SlightlySkewedUnusualData:•Outliersarestragglers:standwayofftothebodyofthedistribution-canbethemostinformativepartofyourdata,oritmightjustbeanerror.Center:•Bestcenterforaskewedgraphoragraphwithoutliers:_______________________________ -resistanttoskewnessandoutliers Valueisliterallyinthemiddle:halfofthevaluesbelowandhalfofthevaluesabovethecenter.

•Bestcenterforabell-shape:________________(_______________will=the____________ifthisisthecase) -_________________isnotresistanttoskewnessandoutliers:itwillgetpulledinacertaindirectionWheneverwefindthecenterofthedata,thenextstepisalwaystoaskhowwellitactuallysummarizesthedata-Weusethespreadtodothis:Spread:•Wheneverwedescribeadistributionnumerically,wealwaysareportameasureofitsspread

alongwithitscenter.(statisticsisaboutvariation,remember?)Range=_______________________________________

•Thespreadhasadisadvantage:Asingleextremevalue(_______________________)canmakeitverylarge,givingitavaluethatdoesn’trepresentthedataoverall.

•Twowaystomeasurespreadaboutthecenter:StandardDeviation(withmean)andIQR(withmedian)

InterquartileRange.(IQR):Abetterwaytodescribethespreadistoignoretheextremesandconcentrateonthemiddleofthedata.YoucandothiswiththeIQR

UnusualData:•Outlier:Anindividualvaluethatfallsoutsidetheoverallpattern

- 1.5xIQRRule- 3standarddeviationsfromthemeanineitherdirection

•Anydataaboveorbelowtwostandarddeviationsfromthemean •Anydatawithhighresidualorleverage(thiswillcomelater)-Wewillfindouthowtocalculatethecenter,spreadsandoutliersinNotes1.3.II.ConstructingDisplaysforQuantitativeDataDotPlot ConstructingaDotPlot-Steps: 1) 2) 3)

Important:Makesureyourx’sordotsarethesamesize,andsamedistanceapartverticallyThedotplotdisplaysdataonthenumberofsiblingsreportedbyeachstudentinastatisticsclass.

UseSUCStodescribethedatadistribution:

ComparingDistributions…betweentwoormoregraphsAPCommonMistakes:1)Needtoaddressallfourcharacteristicsofthedistribution(SUCS)

2) Needtoexplicitlycompareeachcharateristic–discussingSUCSforeachdistributionseparatelywillnotreceivecredit!Usephraseslike:“aboutthesameas”,“ismuchgreaterthan”whencomparingcenterandspread.

Comparethedistributionsofhouseholdsizeforthesetwocountries.*alwayshavescaleslineupwhencomparing.

StemandLeafPlots(Stemplot):Usedtocompareshape/center/spread.Itgivesaquickpictureoftheshapeofthedistribution.ConstructingaStemandLeafPlot-Steps:1)

2)

3)

4)TipstoConsiderBeforeMakingaStemplot:1)2)3)4)Example1:Usetheback-to-backstemplotinFigure1.15towriteafewsentencescomparingthenumberofpairsofshoesownedbymalesandfemales.Besuretoaddressshape,center,spreadandoutliers.Thenanswerthethreemultiplechoicequestions#2-4onpagep.33.

Histograms:Themostcommongraphofthedistributionofonequantitativevariable.ConstructingaHistogram-Steps:1)2)3)Importantthingstoconsiderwhenconstructingahistogram:(summarizetwobulletsonp.35)1)2)Whatarethefourcommonmistakesstudentsmakewithhistograms?1)Whengraphed,thebarshavespacesbetweenthem.Don’tconfusehistogramsandbargraphs!

2)Whengraphed,onlyonenumberisplacedunderbarinsteadof“binningthem”equallywiththesamerange3)Studentoverlapsorgaps:Youneedconsecutive(nogaps),non-overlappingintervals

4)Verticalscaledidn’tstartat0.Usepercentsinsteadofcountsontheverticalaxiswhencomparingdistributionswithdifferentnumberofobservations-scalesshouldbethesametocompare.Example2:ManypeoplebelievethatthedistributionofIQscoresfollowsa“bellcurve”.Butisthisreallyhowthescoresaredistributed?TheIQscoresof60fifth-gradestudentschosenatrandomfromoneschoolareshownbelow:145 139 126 122 125 130 96 110 118 118 101 142 134 124 112109 134 113 81 113 123 94 100 136 109 131 117 110 127 124106 124 115 133 116 102 127 117 109 137 117 90 103 114 139 101 122 105 97 89 102 108 110 128 114 112 114 102 82 101ConstructahistogramthatdisplaysthedistributionofIQscoreseffectively.Thendescribewhatyousee.

(extraspaceforex.4)BoxPlots:Veryhelpfulwhencomparingtwodistributionsthatareskewedorhaveoutliers,andthemedianisusedasacenter.ConstructingaBoxPlot:NeedtheIQRandoutliers,sowesavethisforthenextsectionofnotes.III.GraphingCalculatorTechniques–DisplayingQuantitativeDataHistograms-Practicemakingtheseonyourgraphingcalculator(ps.36-38)

NOTE:OntheAPEXAM-Ifyouareaskedtomakeagraph,besuretolabelandscaleyouraxes.Don’tjusttransferacalculatorscreenshottoyourpaper.BoxPlots:

NOW:CompletethebookassignmentfromSectionIIIonthebackofthispacket.