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1、名称：FundamentalsofStatisticsMeasuresofCentralTendencyandLocation:mean,median,mode,percentiles,quartilesanddeciles.xsortedx53535553705358556457575753586964576868695370TheMeasuresofCentralTendencyareMean,MedianandModeMean—>x-barorx—>foragivenvariable,itisthesumofthevaluesdividedbythenum
2、berofvalues(Lvj/“).Inthiscase,wehave/7=11.Soweneedtoaddallofthevaluestogetheranddivideby11.Z=657,X-59.73Median—>thenumberinadistributionofavariable'sresponsewhereonehalfofthevaluesareaboveandonehalfofthevaluesarebelow.Tofindthemedian,wefirstneedtoputourdatainascendingorder(smallestto
3、largest).Thenwecandeterminethemedian...ifthevalueofnisodd,itissimplythemiddleobservation,butifthevalueofniseven,itistheaverageofthetwomiddleobservations.Inthiscase,nisodd,sothemedianwillbethemiddleobservationofoursortedvalues(the6thvalue)...57Modetthevaluethatoccursmostfrequently.Ift
4、herearetwodifferentvaluesmostfrequentlyoccurring,thedataaresaidtobebi-mcxial.Iftherearemorethantwomodes,andthedistributionissaidtobemulti-modal.Inthiscase,thevaluethatoccursmostoftenis53・So,themodeis53・ThemeasuresoflocationarePercentile,QuartileandDecilePercentiletthepthpercentileisa
5、valuesuchthatatleastppercentoftheobservationsarelessthanorequaltothisvalueandatleast(100-p)percentoftheobservationsaregreaterthanorequaltothisvalue.Tocalculatepercentiles,weuseindices(/)•i=(p/100)nforPl,P2,P3,…P99Iftheanswerisawholenumber(aninteger),theniistheaverageof(P/100)nandJ+(P
6、/100)11.Iftheindexnumberisnotawholenumber,weALWAYSroundup.Thepositionoftheindexisthenextwholenumber(integer)greaterthanthecomputedindex・Forexample:i(pso)=(50/100)11=5・5・“thisroundsupto6So,wewouldcountfromthelowestvalueofthesorteddatatotheindexnumber(6).Sincethecalculatediwasnotawhole
7、numberwehadtorounduptofindthevaluewhereatleast50%ofthevaluesareequaltoorlowerthanthisvalueandatleast50%areequaltoorhigherthanthisvalue・Inthiscase,thevalueofthe50thpercentileisthe6thvalue...57・•・Doesthislookfamiliar?tThe50thpercentileisthesamethingasthemedian.Whatdoesittellus?Inthisdi
8、stribution,A
