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1 Unit14Packet Name: Score: / 1451:DataDisplaysandMeasuresofCentralTendency Statisticsisthesciencesurrounding mostespecially.therearemany waystodisplaydata. Data$Display$$ What$does$it$do?$ $ $ $ $ $ Pictograph Showsdatausing BarGraph Showsdatainspecific CircleGraph Showsdataaspartofa LineGraph Showshowdatachangesover Histogram Showsfrequenciesofdatavalues Stem5and5leafPlot Ordersnumericaldataandhowtheyaredistributed Box5and5WhiskerPlot Showsvariabilityofdatausingquartiles DotPlot Showsthenumberoftimeseach occurs Scatterplot Showstherelationshipbetween datasets Todaywearegoingtofocuson and. ADot$Plotisagraphthatshowsthe (orhowoftenitoccurs)ofeachdata point.dotplotsaregraphedonanumberline.thedataset3,4,4,5,6,6,6,7,8wouldbe graphedas: Ex.$1

2 Arethereanydatapointsthatareverydifferentfromalltheothers?Thesedatapointsarecalled,becausetheylie whatisnormalforthedataset. AHistogramisagraphthatgroupsthedatapoints,itshowsthe of thedatausingintervalsofthe size. Thedataset3,4,4,5,6,6,6,7,8mightbegraphedas: They5axistellsyouhow ofeachthereare. Tocreateahistogramitisimportanttochoosean Appropriatescaleasthex5axisshouldbeacontinuous Numberline. Ex.2$Chooseappropriatescalingandmakeahistogramforthefollowingdatasets: Doeitherofthedatasetsabovehaveoutliers?Howdothetemperaturescompare? Ameasure$of$central$tendencyisa thatrepresentsthe ofadataset.the threemostcommonsmeasuresare,,and.

3 Mean:Themeanofadatasetisthe ofthedata bythenumberofdatavalues. Median:Tofindthemedianorderthedatafrom to.forasetwithan numberofvaluesthemediansisthe value.forasetwithan numberofvalues, themedianisthemeanofthe middlevalues. Mode:Themodeofadatasetisthevalueorvaluesthatoccur often. Eachoneoftheseisanexampleofanaverage.Matchwhichmeasuregoeswithwhichstatement: Theaverageonthetestwasan84 Theaveragetestscoreputsyouinthemiddleoftheclass TheaverageAmericanstudentstartscollegeat18 Ex$3.ThesalariesoftheLALakers(whomakesmorethanamillionayear)forthe season KobeBryant:$30,453,805 PauGasol:$19,285,850 SteveNash:$9,300,500 JordanHill:$3,563,600 ChrisKaman:$3,183,000 JodieMeeks:$1,550,000 MarShonBrooks:$1,210,080 NickYoung:$1,106,942 JordanFarmar:$1,106,942 ChrisDuhon:$1,500,000 Mean:$ $ Median:$ $ Mode:$ Arethereanydatapointsthatyouwouldconsideroutliers?Howdotheyeffectthemean? Takeouttheoutlierandcalculatethenewmean.Howaretheydifferent?Isthisabettermean?

4 1452:BoxandWhiskerPlots Todaywearegoingtofocusonanothertypeofdatadisplay,theBoxandWhiskerPlot.Itiscalled aboxandwhiskerplotbecauseishas andwhatlooklike. InordertouseBox5and5Whiskerplotsweneedtolearnfirstafewvocabularyterms. Quartile:Quartilesmeanyouhavesplityourdatain Range:Thespreadofyourdata,foundbysubtracting 5 =Range 5DNumber$Summary: descriptivenumberthatrepresentthedata,theyare: Minimum$(min):The numberinthedataset 1 st $Quartile$(Q1):"Themedian( )ofthe halfofthedataset Median$(med):Themedian( )ofthedataset 3 rd $Quartile$(Q3):Themedian( )ofthe halfofthedataset Maximum(max):The numberofthedataset Interquartile$Range$(IQR):istherangebetweenQ1andQ3foundbysubtractingQ3"""Q1" ThefivenumbersummaryappearsontheBoxandWhiskerPlotlikethis: Ex.$1Findthefivenumbersummaryforthefollowingdataset:LifeexpectanciesinSouth Americanmales:{59.0,60.5,61.5,66.7,67.9,68.5,69.0,70.3,71.4,71.9,72.1,72.6} Min: Q1:" " " Median: Q3:" " " Max:

5 Findthefivenumbersummaryforthefollowingdataset:LifeexpectanciesinSouthAmerican females:{66.2,66.7,67.7,72.8,74.3,74.4,74.6,76.5,76.6,78.8,79.0,79.4} Min: Q1:" " " Median: Q3:" " " Max: Tocreateaboxandwhiskerplot: 15 anumberlinethatisappropriatelyscaledforyoudata 25 thefive5numbersummary,{min,q1,median,q3,max} 35 arectangularboxfromq1,toq3,witha lineatthemedian 45 linesegments( )fromthemaxandmintotheirrespectivequartiles Drawaboxplotforeachofthefivenumbersummariesabove: Males: Females: Findtherangeandinterquartilerangeoftheabovedatasets: Males Females Range: Range: IQR: IQR: Istherangeheavilyaffectedbyasinglepoint?IstheIQRheavilyaffectedbyasinglepoint? Whichwouldbemorelikelytobeaffectedbyanoutlier?

6 Boxandwhiskerplotsallowustogetagoodvisualofoutliers:aumberthatmakesoneofthe noticeablylongerthantheother.ruleforoutliers:anumberisconsideredan outlierifitismorethan1.5 IQR Q1or Q3."" Ex.$2BelowisthefivenumbersummaryforRogerMaris homerundata.is61anoutlier? {5,11,19.5,30.5,61} Whatdoesthatmeanabouthishomeruns? Thelasttwothingswewilltalkaboutaredistributionandspread.Therearethreetypesof distribution. Skewed$left:Mostofthedataisonthe,theleftwhiskeris thantheright Skewed$right:Mostofthedataisonthe,therightwhiskeris thantheleft Normal/Symmetric:Medianisinthe middleofthedata,whiskersarethe length Spread:Spreadhastodowiththe and,isoneboxbiggerthantheother? Labelthefollowingaccordingtotheirdistributionandspread: Alltypesofdatadisplayshavedistributionandspread,itisaboutlookingfromthecenterofthe dataanddeterminingwheremostofyourdatais.

1453:Two5WayFrequencyTables Statisticsareoftenusedtodescribecategoricaldata.Categoricaldataisdatacollectedregarding insteadofspecificnumbers.

Whenwetalkabouttwo5waytablesweoftentalkabouttwoideasbeingcorrelated.Correlation istherelationshipbetween variables.

7 1453:Two5WayFrequencyTables Statisticsareoftenusedtodescribecategoricaldata.Categoricaldataisdatacollectedregarding insteadofspecificnumbers.atwodway$frequencytabledisplays categoriesofdatacollectedfromthe source.eachentryinthetableiscalleda. Whenwetalkabouttwo5waytablesweoftentalkabouttwoideasbeingcorrelated.Correlation istherelationshipbetween variables.ifitseemslikeasonevariable the other thenthetwovariablesare correlated.ifitseemslikeas onevariable theother thenthereisa correlation.if thereseemstobenorelationshipatallthentheyare correlated. Readingatwo5waytable: The oftherowsandcolumnsarecalled frequencies. Ex.$1

8 Makingatwowaytable:Istherearelationshipbetweenpreferredhandandpreferredeye?Are peoplewhoconsiderthemselves lefthanded morelikelytobe lefteyed? Whichismorelikelyforourclassdata,someonetobeleft5handedorright5handed?Howdoyou know? Whichismorelikelyforourclassdata,someonetobeleft5eyedorright5eyed?Howdoyou know? Whichismorelikelyfortheleft5handedpeople,tobeleft5eyesorright5eyed?Howdoyouknow? Whichismorelikelyfortheright5handedpeople,tobeleft5eyesorright5eyed?Howdoyou know? Doyouthinkthereisacorrelationbetweenpreferredhandandpreferredeye? Wecanalsousetwo5wayfrequencytablestoanswerquestionsregardinganentirepopulation. Doyouthinkthereisacorrelationbetweenusingconditionerandbeingfemale? $ $ $ $ $ $ $ $ $ $ Total Total $ $ Conditioneruse Use Don tuse conditioner conditioner Total Male Gender Female 14 1 Total Fillinthetotalsabove.Todeterminepercentagesbasedoffofatwowaytablewewillneedto decidewhichtovaluesthequestionwantsustocompare.thentofindapercentwesimply dividethetwo.

9 15Whatpercentofthegroupismale? Keywords:groupandmale,whichitemsinourtablerepresenttheamountofmalesandthe amountinthegroup? Percent: 25Whatpercentofthegroupismalethatusedconditioner? Keywords: Percent: 35Whatpercentofthegroupusesconditioner? Keywords: Percent: 45Whatpercentofthefemalesuseconditioner? Keywords: Percent: 55Whichgrouphasahigherpercentageusingconditioner? Keywords: Percent: 65Aretheremoremalesormorefemalesthatuseconditioner? 75Doyouthinkthereisacorrelationbetweenconditioneruseandbeingfemale? 1454:StandardDeviation Thestandard$deviationofadatasetistheaveragedistanceeachpointisfromthemean.This tellsyouhowspreadyourdatais. Wefindstandarddeviationonourcalculators: 15 HittheSTATbutton,undertheeditmenuselect1:Edit (shouldbewhatthemenuopens youto) 25 ClearL1byputtingyourcursorontheL1andselectingCLEAR,thenenteryourdatainto L1 35 ClickontheSTATbuttonagain,thistimeuseyourcursortogototherighttotheCALC menu,thenhitenter(thisselects15varstats) 45 Thiswilltakeyoubacktothemainscreenwith15VarStatsonyourscreen.Thenhit ENTER,Standarddeviationistheσ x = Findthestandarddeviationof70,70,75,75,90,70,80,85,65,95,70,85,90,70,20 σ x =

10 Secondary*1 Name: In-*Class* 14*1DatadisplaysandMeasuresofCentralTendency 3.Doeitherofthesetshaveoutliers?Comparingthetwosetshowtotheagesofthekidsat thepartycomparetotheagesofthestudentsinthecollegeclass? 4.Makeahistogramofthefollowingdata:Numberofdegreesover100degreesinvarious states:12,10,7,16,20,0,18,12,8,13,27,17,14,10,20

11 5.U.S.Presidentshaveenteredintoofficeatmanydifferentages.Thetablebelowdisplays thenumberofpresidentsinauguratedwithindifferentagegroups.usethedatato createahistogram. 6.Labelthefollowingasmean,medianormode: Theaveragetestscorewasa78. Heraverageofherlongandshortprogramputherinthemiddleoftherankings. TheaverageAmericanFemaleis5 6. Findthemean,medianandmodeforthefollowing: 7.pricesindollarsofsmartphones:311,309,312,314,399,312 8.attendanceataneventforthelastnineyears:68,99,73,65,67,62,80,81,83 9.booksastudentchecksoutofthelibrary:17,9,10,17,18,5,2 10.Findthemeanofthedata,thenremovetheoutlierandfindthenewmean.Howdothey differ?whichoneisabettermeasureofthecenter?repaircostsat5mph: AudiA6:0 BMW328i:0 CadillacCatera:900JaguarX:1254 LexusES300:234 LexusIS300:979 MercedesC320:707 Saaab9*5:670 VolvoS60:769 VolvoS80:4194

Secondary*1 Name: In-*Class* 14*2BoxandWhiskerPlots Findthefivenumbersummaryforthefollowingdatasetsandthenconstructabox*plot 1.pricesindollarsofsmartphones:311,309,312,314,399,312 2.

12 Secondary*1 Name: In-*Class* 14*2BoxandWhiskerPlots Findthefivenumbersummaryforthefollowingdatasetsandthenconstructabox*plot 1.pricesindollarsofsmartphones:311,309,312,314,399,312 2.attendanceataneventforthelastnineyears:68,99,73,65,67,62,80,81,83 3.booksastudentchecksoutofthelibrary:17,9,10,17,18,5,2 4.Giventhefivenumbersummary:{0.3,1.0,2.6,4.5,17.1}(SalariesofNBAteamsinMillions) Findtherange: FindtheIQR: Is17.1anoutlier? 5.Identifytheshapeand spreadofeachdistribution YourClass: Yourfriend sclass:

13 6. 7/8. Determineifthedataisskewedright,skewedleft,orsymmetric

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