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1、外文翻译原文名称:Fundamentals_of_StatisticsMeasuresofCentralTendencyandLocation:mean,median,mode,percentiles,quartilesanddeciles.xsortedx53535553705358556457575753586964576868695370TheMeasuresofCentralTendencyareMean,MedianandModeMean®x-baror®foragivenvariable,itisthesumofthevaluesdividedbythenumbero
2、fvalues(Sxi/n).Inthiscase,wehaven=11.Soweneedtoaddallofthevaluestogetheranddivideby11.S=657,=59.73Median®thenumberinadistributionofavariable’sresponsewhereonehalfofthevaluesareaboveandonehalfofthevaluesarebelow.Tofindthemedian,wefirstneedtoputourdatainascendingorder(smallesttolargest).Thenwec
3、andeterminethemedian…ifthevalueofnisodd,itissimplythemiddleobservation,butifthevalueofniseven,itistheaverageofthetwomiddleobservations.Inthiscase,nisodd,sothemedianwillbethemiddleobservationofoursortedvalues(the6thvalue)...57Mode®thevaluethatoccursmostfrequently.Iftherearetwodifferentvaluesmo
4、stfrequentlyoccurring,thedataaresaidtobebi-modal.Iftherearemorethantwomodes,andthedistributionissaidtobemulti-modal.Inthiscase,thevaluethatoccursmostoftenis53.So,themodeis53.ThemeasuresoflocationarePercentile,QuartileandDecilePercentile®thepthpercentileisavaluesuchthatatleastppercentoftheobse
5、rvationsarelessthanorequaltothisvalueandatleast(100–p)percentoftheobservationsaregreaterthanorequaltothisvalue.Tocalculatepercentiles,weuseindices(i).i=(p/100)nforp1,p2,p3,…p99Iftheanswerisawholenumber(aninteger),theniistheaverageof(P/100)nand1+(P/100)n.Iftheindexnumberisnotawholenumber,weALW
6、AYSroundup.Thepositionoftheindexisthenextwholenumber(integer)greaterthanthecomputedindex.Forexample:i(p50)=(50/100)11=5.5...thisroundsupto6So,wewouldcountfromthelowestvalueofthesorteddatatotheindexnumber(6).Sincethecalculatediwasnotawholenumberwehadtorounduptofindthevaluewhereatleast50%ofthev
7、aluesareequaltoorlowerthanthisvalueandatleast50%areequaltoorhigherthanthisvalue.Inthiscase,thevalueofthe50thpercentileisthe6thvalue...57…Doesthislookfamiliar?®The50thpercentileisthesamethingasthemedian.Whatdoesittellus?Inthisdistribution,ATLE