商务统计公式总结

SamplemeanQ1at(n+1)/4Q2at(n+1)/2(themedianposition)Q3at3(n+1)/4Interquartilerange=Q3–Q1Samplevariance1-n)X(X....)X(X)X(X1-n)X(XS2n2221n1i2i2Samplestandarddeviation1-n)X(Xn1i2isCoefficientofVariation100%XSCVZScoreSXXZPopulationmeanNXXXNXNNii211PopulationvarianceNμ)(XσN1i2i2PopulationstandarddeviationNμ)(XσN1i2iChebyshevRule:atleast(1-1/k2)x100%ofthevalueswillfallwithinμ±kσP(AorB)=P(A)+P(B)-P(AandB)P(B)B)andP(AB)|P(ATwoeventsareindependentifandonlyif:P(A)B)|P(AP(B)B)|P(AB)andP(AP(B)P(A)B)andP(A(IfAandBareindependent)selectXobjectsfromnobjects:X)!(nX!n!Cxn(numberofdifferentways)nXXXnXXnnii211selectandarrange:X)!(nn!PxnExpectedValue(mean)(discretedistribution))()()()(E(X)nn22111XPXXPXXPXXPXNiiiVarianceofadiscreterandomvariableN1ii2i2)P(XE(X)][XσStandardDeviationofadiscreterandomvariableN1ii2i2)P(XE(X)][Xσσxn-xnxPX=Cp1-p（）(Xsuccessesinntrials)BinomialDistributionMeannpE(x)μVariancep)-np(1σ2StandardDeviationp)-np(1σDiscreteProbabilityDistributions!)(XeXPx(=expectednumberofevents;e=2.71828...)PoissonDistributionMeanλμVarianceλσ2StandardDeviationλσStandardizedNormalDistributiontranslationσμXZμμXoftheMeanX(isnormalifpopulationisnormalorn30)SamplingDistributionsoftheProportion(normaldistributionif5)n(15nandππ)σisKnownforthePopulationMean,μConfidenceIntervalsσisUnknownConfidenceIntervalsforthePopulationProportion,πformeanDeterminingSampleSizeforproportionπcanbeestimatedwithapilotsample(orconservativelyuseπ=0.5)nσσXnσμ)X(σ)μX(ZXXπpμn)(1σpππn)(1pσpZpnσZXnStX1-nnp)p(1ZpnσZe222σeZnn)(1Zeππ22e)(1Znππ