Copyright©2009CengageLearning4.1ChapterFourNumericalDescriptiveTechniquesCopyright©2009CengageLearning4.2NumericalDescriptiveTechniques…MeasuresofCentralLocationMean,Median,ModeMeasuresofVariabilityRange,StandardDeviation,Variance,CoefficientofVariationMeasuresofRelativeStandingPercentiles,QuartilesMeasuresofLinearRelationshipCovariance,Correlation,Determination,LeastSquaresLineCopyright©2009CengageLearning4.3MeasuresofCentralLocation…Thearithmeticmean,a.k.a.average,shortenedtomean,isthemostpopular&usefulmeasureofcentrallocation.Itiscomputedbysimplyaddingupalltheobservationsanddividingbythetotalnumberofobservations:SumoftheobservationsNumberofobservationsMean=Copyright©2009CengageLearning4.4Notation…Whenreferringtothenumberofobservationsinapopulation,weuseuppercaseletterNWhenreferringtothenumberofobservationsinasample,weuselowercaseletternThearithmeticmeanforapopulationisdenotedwithGreekletter“mu”:Thearithmeticmeanforasampleisdenotedwithan“x-bar”:Copyright©2009CengageLearning4.5ArithmeticMean…PopulationMeanSampleMeanCopyright©2009CengageLearning4.6TheArithmeticMean……isappropriatefordescribingmeasurementdata,e.g.heightsofpeople,marksofstudentpapers,etc.…isseriouslyaffectedbyextremevaluescalled“outliers”.E.g.assoonasabillionairemovesintoaneighborhood,theaveragehouseholdincomeincreasesbeyondwhatitwaspreviously!Copyright©2009CengageLearning4.7MeasuresofCentralLocation…Themedianiscalculatedbyplacingalltheobservationsinorder;theobservationthatfallsinthemiddleisthemedian.Data:{0,7,12,5,14,8,0,9,22}N=9(odd)Sortthembottomtotop,findthemiddle:005789121422Data:{0,7,12,5,14,8,0,9,22,33}N=10(even)Sortthembottomtotop,themiddleisthesimpleaveragebetween8&9:00578912142233median=(8+9)÷2=8.5Sampleandpopulationmediansarecomputedthesameway.Copyright©2009CengageLearning4.8MeasuresofCentralLocation…Themodeofasetofobservationsisthevaluethatoccursmostfrequently.Asetofdatamayhaveonemode(ormodalclass),ortwo,ormoremodes.Modeisausefulforalldatatypes,thoughmainlyusedfor...
