Class 4- Central Tendency and Spread

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1、9/27/2012MEASURESOFCENTRALFangChenECNUTENDENCY&VARIABILITY陈芳StatisticsforLanguageResearch华东师大英语系Class4Fall20121REVIEW9/27/2012Rulesofdatadisplaying1.Ifitaidsunderstanding,doit;ifitdoesn’t,don’t.FangChenECNU2.Keepthingssimple.陈芳华东师大英语系2DISTRIBUTION9/27/2012FangChenECNU陈芳

2、华东师大英语系3DESCRIBINGDISTRIBUTION9/27/2012SymmetryModalityFangChenECNUSkewnessKurtosisf陈芳华东师大英语系Figure3.9and3.10Page524REVIEWOFHISTOGRAM---SEEINGTHESHAPE9/27/2012GPAFangChenECNU5160Skew?140Modality?120100Kurtosis?陈芳华东师大英语系806040Std.Dev=.6620Mean=2.79Frequency0N=1901.0

3、0.38.63.881.131.381.631.882.132.382.632.883.133.383.633.88GPA9/27/2012FangChenECNU陈芳华东师大英语系CHAPTER46MeasuresofCentralTendency集中趋势9/27/2012Whenyouaskyourcolleagueteacherswhatthestudentsaredoinginhisorherclass,yousayFangChenECNU“___________________________________?”Onem

4、ajorpurposeofstatisticalproceduresisto陈芳summarizerawdatainameaningfulwaysothat华东师大英语系wecanaccuratelydescribeoursampleorpopulationanddrawconclusionsStatisticsthatdescribecentraltendencyarenumericalvaluesthatdescribethecenterofa7distributionofscoresforavariable.CENTRALTE

5、NDENCY9/27/2012Threecommonmeasuresofcentraltendency:FangChenECNUMode众数Median中数陈芳Mean平均数华东师大英语系8FINDINGTHEMODE众数9/27/2012Createafrequencydistributionforasetofvaluesandfindthevaluethatoccursmostfrequently.FangChenECNUValueN%1211.8215.9315.94211.8陈芳5317.6华东师大英语系6423.5

6、7211.8815.9915.9Total17100X={1,7,6,4,6,3,8,4,6,5,2,5,6,9,1,5,7}9FINDINGTHEMEDIAN中数9/27/2012X={1,1,2,3,4,4,5,5,6,6,6,6,7,7,8,9}FangChenECNU陈芳X={1,1,2,3,4,4,5,5,6,6,6,7,7,8,9}华东师大英语系10THEMEAN/AVERAGE平均数9/27/2012themostcommonmeasureofcentraltendencyFangChenECNUDefinedast

7、heaverageofalltheobservedscore.Usuallyhastobecalculated.陈芳Thestatisticalnotationforthemeanis:华东师大英语系µwhenwearedealingwithpopulationsXwhenwearedealingwithsamples∑XWecalculatethemeanwith:X=N11COMPAREANDCONTRAST9/27/2012Themoresymmetricadistributionis,thecloserthesethr

8、eemeasuresofcentralFangChenECNUtendencywillbeIfadistributionistrulynormal(symmetric陈芳andunimodal),thenthemean