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1、DescriptiveStatistics:NumericalMethodsChapter3DescriptiveStatistics:NumericalMethodsLearningObjectives1.Understandthepurposeofmeasuresoflocation.2.Beabletocomputethemean,median,mode,quartiles,andvariouspercentiles.3.Understandthepurposeofmeasuresofvariability.4.Beabletocomputetherange,interqu
2、artilerange,variance,standarddeviation,andcoefficientofvariation.5.Understandhowzscoresarecomputedandhowtheyareusedasameasureofrelativelocationofadatavalue.6.KnowhowChebyshev’stheoremandtheempiricalrulecanbeusedtodeterminethepercentageofthedatawithinaspecifiednumberofstandarddeviationsfromthe
3、mean.7.Learnhowtoconstructa5-numbersummaryandaboxplot.8.Beabletocomputeandinterpretcovarianceandcorrelationasmeasuresofassociationbetweentwovariables.9.Beabletocomputeaweightedmean.3-29DescriptiveStatistics:NumericalMethodsSolutions:1.10,12,16,17,20Median=16(middlevalue)2.10,12,16,17,20,21Med
4、ian=3.15,20,25,25,27,28,30,322ndposition=206thposition=284.Median=576thitemMode=53Itappears3times5.a.b.Thereareanevennumberofitems.Thus,themedianistheaverageofthe15thand16thitemsafterthedatahavebeenplacedinrankorder.Median=c.Mode=36.4Thisvalueappears4times3-29DescriptiveStatistics:NumericalMe
5、thodsd.FirstQuartileRoundingup,weseethatQ1isatthe8thposition.Q1=36.2e.ThirdQuartileRoundingup,weseethatQ3isatthe23rdposition.Q3=37.96.a.Medianisaverageof10thand11thvaluesafterarranginginascendingorder.Dataaremultimodalb.Mode=70(4brokerscharge$70)c.Comparingallthreemeasuresofcentrallocation(me
6、an,medianandmode),weconcludethatitcostsmore,onaverage,totrade500sharesat$50pershare.d.Yes,trading500sharesat$50pershareisatransactionvalueof$25,000whereastrading1000sharesat$5pershareisatransactionvalueof$5000.7.a.b.Yes,themeanhereis46minutes.Thenewspaperreportedonaverageof45minutes.c.d.Q1=7(
7、valueof8thiteminrankedorder)Q3=70.4(valueof23rditeminrankedlist)e.Findposition40thpercentileisaverageofvaluesin12thand13thpositions.3-29DescriptiveStatistics:NumericalMethods8.a.=775Themodalageis29;itappears3times.b.Medianisaverageof10thand11
