均数和标准差

MedicalStatistics(fullEnglishclass)Ji-QianFangSchoolofPublicHealthSunYat-SenUniversityChapter9StatisticalAnalysisForMeasurementDataprofile轮廓Symmetric对称Skew偏倚Positiveskew正偏倚negativeskew负偏倚Centralposition中心位置Variability变异性Outliers异常值ArithmeticMean算术均数Geometricmean几何均数Median中位数rawdata原始资料Variance方差StandardDeviation标准差NumericalDescriptionCentralposition(centraltendency)Variation(measureofdispersion)2.MeasuresforAverage(1)ArithmeticMeanBasedonobserveddataExample:Bloodsugar6.2,5.4,5.7,5.3,6.1,6.0,5.8,5.9nXnXnXXXXniin121...8.584.4689.5...4.52.6XBasedonfrequencytablenfXnXffffXfXfXfXniiinnn11212211......Table9-3Frequencytableoftheurineacidfor20-29yearsoldmalesConcentration(mol/L)Mid-value(xi)Frequency(fi)fixifixi2270-277.52550.0154012.5285-292.592632.5770006.3300-307.5113382.51040119.0315-322.5227095.02288138.0……………420-435427.51427.5182756.0Totalfi=150fixi=52470.0fixi2=18518738.0)/(8.349150524702...325.4271...5.29295.2772LmolX(2)GeometricmeanExample9-4SeeTable9-4)lg(lg)lg...lglg(lg121121nXnXXXGXXXGnnn(3)MedianRankingthevaluesofobservationfromthesmallesttothelargest,Median=thevalueinthemiddleBasedonrawdataExample1:(7values)120,123,125,127,128,130,132Median=127Example2:(8values)118,120,123,125,127,128,130,132Median=(125+127)/2=12621.19)81%50308(9525)%50(?Lfnfi21.6921.1950?5050PFrequency95Lf154%50n176ffLInterval50L?5050P75iLBasedonFrequencyTableTable9-5Frequencytableofurineacidforchildrenunder6yearsoldUrinelead(mmol/L)(1)Frequencyf(2)Cumulativefrequencyf(3)Cumulativerelativefrequency(4)=(3)/n0-27278.7725-548126.3050-9517657.1475-5523175.00…………175-5308100.0Total308(fi)----SymmetricRBC(10/L)of130normalmaleadultsinaplace3.844.24.44.64.855.25.45.65.8RBC(10/L)051015202530FrequencyPositiveskewHairMercury(ug/g)of238normaladults0.50.91.31.72.12.52.93.33.74.1Hg(ug/g)010203040506070FrequencyThinkaboutHowtocalculateP25?basedonrawdata?basedonfrequencytable?HowtocalculateP75?basedonrawdata?basedonfrequencytable?Summary1.Mean:Suitabletosymmetricdistribution.2.Geometricmean:Suitabletopositiveskewdistribution3.Median:Suitabletoallkindsofdata,butpoorattributeforfurtheranalysis3.Measuresforvariability(1)RangeRange=Maximum-MinimumBasedononlytwoobservations,itignorestheobservationswithinthetwoextremes.Thegreaterthenumberofobservations,thegreatertherangeis.(2)Inter-quartilerangeLowerQuartile:25percentileUpperQuartile:75percentileDifferencebetweentwoQuartiles=UpperQuartile-LowerQuartile=13.120–8.083=5.03715.48)27%25308(54252525P0.100)176%75308(55257575PTable9-5Frequencytableofurineacidforchildrenunder6yearsoldUrinelead(mmol/L)(1)Frequencyf(2)Cumulativefrequencyf(3)Cumulativerelativefrequency(4)=(3)/n0-27278.7725-548126.3050-9517657.1475-5523175.00…………175-5308100.0Total308(fi)----(3)VarianceandStandardDeviationThemeanofsquareddeviationStandarddeviation(SD)nX22)(1)(1)(2222nnXXnXXs22ssExample9-8Theweightofmaleinfant2.85,2.90,2.96,3.00,3.05,3.18(1)117.001368.001368.050684.016)99.218.3(...)99.290.2()99.285.2(2222ss1)(12nXXsnii2/)(1212nnXXsniinii117.0166/)94.17(709.532s(2)(4)CoefficientofVariationXsCVExample9-10VariationofheightandvariationofweightMean(1)Standarddeviation(2)CoefficientofVariation(%)(3)=(2)/(1)Height171.21(cm)5.34(cm)3.12Weight59.72(kg)4.16(kg)6.97