summary statistics（商务统计英文版） ppt课件

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1、BusinessStatisticsBEO1106WEEK2NUMERICALSUMMARYSTATISTICSReference:Selvanathanetal.(2004),Chapters2,3.1BEO1106-Week2NUMERICALSUMMARYMEASURESNumericalsummarymeasuresdescribethemajorpropertiesofadataset,namelyits:centraltendency(orlocation),variability(ordispe

2、rsion,spread),shape.1.MEASURESOFCENTRALTENDENCYTheylocatethe‘centrality’ofthedataset.Arithmeticmean(variableX)Forthepopulation:(mu)Forasample:x-barAddupthevaluesDividebythenumberofvaluesPopulationsizeSamplesize2BEO1106-Week2Propertiesofthemean:Itisthemostc

3、omprehensivemeasureofcentrallocation(i.e.itiscomputedfromallavailabledatavalues);Eachquantitativedatasethasoneandonlyonemean;The(sample)meanisusedextensivelyininferentialstatistics;Itcanbedistortedbyoutliers(orextremevalues).Uncharacteristicallysmallorlarge

4、values.Median:Themiddlevalueofanorderedarray.3BEO1106-Week2Howtofindthemedian‘manually’?Sortthedatafromsmallesttolargest.Choosethemiddlevalueifn(N)isodd,ortaketheaverageofthetwomiddlevaluesifn(N)iseven.Propertiesofthemedian:Eachquantitativedatasethasoneando

5、nlyonemedian;Itisunaffectedbyoutliers;Itiscomputedfromatmosttwodatapoints;Ithaslimitedapplicationandmathematicalpotential.Mode:Themostfrequentlyoccurringvalueofadataset.Propertiesofthemode:Itcanbeusedtodescribebothquantitativeandqualitativedata;Itisunaffect

6、edbyoutliers;Itmightnotbeuniqueoruseful;Ithaslimitedapplicationandmathematicalpotential.4BEO1106-Week22.MEASURESOFVARIABILITY(DISPERSION)Howmuchisthedataspreadoutarounditscentre?Range:largest–smallestPropertiesoftherange:Eachquantitativedatasethasoneandonly

7、onerange;Itiscomputedfromonlytwodatapoints;Itisaffectedbyoutliers;Ithaslimitedapplicationandmathematicalpotential.Variance:‘average’ofthesquareddeviationsfromthemean.Forthepopulation:2(sigma)Forasample:s2SumofsquareddeviationsdividedbyN,n-15BEO1106-Week2Pr

8、opertiesofthevariance:Eachquantitativedatasethasoneandonlyonevariance;Itisacomprehensivemeasureofdispersion;Itisaffectedbyoutliers;Itisconceptuallycomplicated;Itishardtointerpretsinceitisgivenin‘square