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1、生物统计学学习笔记（1）描述性统计DescriptiveStatistics位置测度法measureoflocationOnetypeofmeasureusefulforsummarizingdatadefinesthecenter,ormiddle,ofthesample.Thistypeofmeasureisameasureoflocation.算术平均数：arithmeticmeanThearithmeticmeanisthesumofalltheobservationsdividedbythenumberofobservations.Itiswritteninsta
2、tisticaltermsas算术平均是的缺点是对极端是太敏感了。在这种情况下他不能代表样本的绝大多数。Thearithmeticmeanis,ingeneral,averynaturalmeasureoflocation.Oneofitsmainlimitations,however,isthatitisoversensitivetoextremevalues.Inthisinstance,itmaynotberepresentativeofthelocationofthegreatmajorityofsamplepoints.中位数medianSupposetherea
3、renobservationsinasample.Iftheseobservationsareorderedfromsmallesttolargest,thenthemedianisdefinedasfollows:1.The（n+12）thlargestobservationifnisodd2.Theaverageofthe（n2）thand（n2+1）thlargestobservationsifniseven众数modeThemodeisthemostfrequentlyoccurringvalueamongalltheobservationsinasample.几何
4、平均数TheGeometricMeanThegeometricmeanistheantilogarithmoflogx,where离散性测度MeasuresofSpread极差range一个样本中最大值和最小值之间的差异Therangeisthedifferencebetweenthelargestandsmallestobservationsinasample分位数Thepthpercentileisdefinedby(1)The(k+1)thlargestsamplepointifnp/100isnotaninteger(wherekisthelargestintege
5、rlessthannp/100).(2)Theaverageofthe(np/100)thand(np/100+1)thlargestobservationsifnp/100isaninteger.Percentilesarealsosometimescalledquantiles.R可以如下求解>quantile(pzcz$BornAlive)0%25%50%75%100%08101220>quantile(pzcz$BornAlive,probs=c(0.1,0.9),na.rm=TRUE,type=2)10%90%613>quantile(pzcz$BornAlive
6、,probs=c(0.1,0.25,0.5,0.75,0.9),na.rm=TRUE,type=2)10%25%50%75%90%68101213方差与标准差TheVarianceandStandardDeviationThesamplevariance,orvariance,isdefinedasfollows:S2=i=1n(xi-x)n-1Arationaleforusingn−1inthedenominatorratherthannispresentedinthediscussionofestimationinChapter6.Thesamplestandardde
7、viation,orstandarddeviation,isdefinedasfollows:S=i=1n(xi-x)n-1=samplevariance分组数据GroupedDataAfrequencydistributionisanordereddisplayofeachvalueinadatasettogetherwithitsfrequency,thatis,thenumberoftimesthatvalueoccursinthedataset.Inaddition,thepercentageofsampl
