Summarystatistics1Inthischapter:weintroduce,asmeasuresoflocationoraverageforacollectionofdata,themedian,themean,theweightedmeanandthegeometricmeanweextendthemethodsofpresentingdatatoincludefrequencytablesandcumulativefrequencypolygonsweanalysesymmetryindataanddefineskewnessWhatdoweneedtoknowConsiderthedatapresentedinthestem-and-leafdiagrambelow(unitis1).099991373725825847351593743208456253586964187748391047118Thisisadisplayofthetime,inseconds,takenby43carstopassthroughacontinentalmotorwaytollsection.Whatwouldanexperimenterneedtotakeintoaccountwhencollectingthisinformation?WhatweneedtoknowAmongthemanyconsiderations,itwouldbeimportanttohavesomeideasofwhatatypicaltimewaslikelytobe,andthelikelyrangeoftimes.Thisinformationisnecessarysothatanappropriatetimingdevicecanbeselected.Therewouldbelittlepointintryingtouseawatch’sminutehandoranelectronictimercapableofrecordingto1/1000ofasecond.Itisalsounlikelytobenecessarytorecordtimesaslongasanhour,butthetimerneedstobecapableofrecordingmorethanafewseconds.Therearetwomeasuresrepresentativeofdatawhichmaybeusefulincaselikethis–onerepresentingthe‘typicalvalue’andanotherwhichindicatesthe‘sortofrangeofvalue’likelytobefound.Instatisticalterms,thesearemeasuresoflocationoraverageanddispersionorspread.Lifewouldbesimpleiftherewerejustoneofeach,orevenanidealmeasureofeachquality.Unfortunately,thisisnotthecase.Therearemanytypesofaverageandseveralkindsofspread.Inthischapterweshallconcentrateonaverages.ModeThemodeisthemostcommonlyoccurringvalueoritemofdate,or,inotherwords,theonethatappearsmostfrequently.Inthecontextofthedataunderconsideration,themostcommonlyoccurringvalueis9seconds.Isitreasonable,though,toconsider9secondsasbeingtypicalofthetimetakentopassthroughthiscontinentalmotorwaytoll?Almostcertainlynot!Itmanybemoreappropriatetoconsiderthemodalclass.Referringbacktothediagram,the1-branchhasthegreatestfrequency.Hence,itwouldbereasonabletosaythatthemodeisthetimebetween20and30seconds.Thisisthelongestbranchinthestem-and-leafdiagram...
