外文翻译原文名称：Fundamentals_of_Statistics---本文来源于网络，仅供参考，勿照抄，如有侵权请联系删除---MeasuresofCentralTendencyandLocation:mean,median,mode,percentiles,quartilesanddeciles.xsortedx53535553705358556457575753586964576868695370TheMeasuresofCentralTendencyareMean,MedianandModex?foragivenvariable,itisthesumofthevaluesdividedbythenumberMean?x-barorofvalues(?x/n).Inthiscase,wehaven=11.Soweneedtoaddallofthevaluestogetherandix=59.73=657,?divideby11.Median?thenumberinadistributionofavariable'sresponsewhereonehalfofthevaluesareaboveandonehalfofthevaluesarebeloTofindthemedian,wefirstneedtoputourdatainascendingisitodd,isnofevaluthemedian…ifthedeterminecanweThenlargest).to(smallestordersimplythemiddleobservation,butifthevalueofniseven,itistheaverageofthetwomiddleobservations.thvalue)...57isodd,sothemedianwillbethemiddleobservationofoursortedvalues(the6nInthiscase,Mode?thevaluethatoccursmostfrequently.Iftherearetwodifferentvaluesmostfrequentlyoccurring,thedataaresaidtobebi-modal.Iftherearemorethantwomodes,andthedistributionissaidtobemulti-modal.Inthiscase,thevaluethatoccursmostoftenis53.So,themodeis53.ThemeasuresoflocationarePercentile,QuartileandDecile---本文来源于网络，仅供参考，勿照抄，如有侵权请联系删除---thpercentileisavaluesuchthatatleastp?theppercentoftheobservationsarelessthanPercentileorequaltothisvalueandatleast(100–p)percentoftheobservationsaregreaterthanorequaltothisvalue.Tocalculatepercentiles,weuseindices(i).i=(p/100)nforp,p,p,…p99132Iftheanswerisawholenumber(aninteger),theniistheaverageof(P/100)nand1+(P/100)n.Iftheindexnumberisnotawholenumber,weALWAYSroundup.Thepositionoftheindexisthenextwholenumber(integer)greaterthanthecomputedindex.Forexample:i=(50/100)11=5.5...thisroundsupto6(p50)So,wewouldcountfromthelowestvalueofthesorteddatatotheindexnumber(6).Sincethecalculatediwasnotawholenumberwehadtorounduptofindthevaluewhereatleast50%ofthevaluesareequaltoorlowerthanthisvalueandatleast50%thpercentileInthiscase,thevalueofthe50areequaltoorhigherthanthisvalue.ththpercentileisthesameThe50value...57…Doesthislookfamiliar??isthe6thingasthemedian.Whatdoesittellus?Inthisdistribution,ATLEAST50%oftheobservationsareLESSTHANOREQUALTO57ANDATLEAST50%oftheobservationsareGREATERTHANOREQUALTO57.thvalueis68.The9=(80/100)11=8.8...thisroundupto9.i(p80)Again,sincetheindexnumberisnotawholenumber,weroundup.So,wewouldcountfromthelowestvalueofthesorteddatatotheindexnumber(9).Inthiscase,thevalueofthethpercentileis68.80Sincethisdatasethas11observations,wewon'thaveanyinstanceswhereourcalculatedindexnumberisawholenumber.However,ifwejustremoveourvalueof70andcreateanewdistribution,wewillbeabletoseeanexample...53535355575758646869rdthvaluesandand4i=(30/100)10=3...thisisawholenumber,sowemusttakethe3(p30)thpercentile.(53+55)/2=54averagethemtofindthe30thpercentileis54.---本文来源于网络，仅供参考，勿照抄，如有侵权请联系删除---So,thevalueofthe30Returntoouroriginaldatadistribution...Quartiles–arespecialcasesofpercentiles…Q=P,Q=P,Q=P,755021253Thesethreevaluesdividethedistributioninto4equalquartersrdvalue...532.75...thisroundsto3,soQ1isthe3i=(25/100)11=(Q1)thvalue...57=(50/100)11=5.5...thisroundto6,soQ2isthe6i(Q2)．th=(75/100)11=8.25...thisroundsto9,soQ3isthe9value...64i(Q3)Range,interquartilerange(IQR),variance,standarddeviationMeasuresofDispersi...