商务与经济统计习题答案（第8版，中文版）SBE8-SM03

3-1Chapter3DescriptiveStatistics:NumericalMethodsLearningObjectives1.Understandthepurposeofmeasuresoflocation.2.Beabletocomputethemean,median,mode,quartiles,andvariouspercentiles.3.Understandthepurposeofmeasuresofvariability.4.Beabletocomputetherange,interquartilerange,variance,standarddeviation,andcoefficientofvariation.5.Understandhowzscoresarecomputedandhowtheyareusedasameasureofrelativelocationofadatavalue.6.KnowhowChebyshev’stheoremandtheempiricalrulecanbeusedtodeterminethepercentageofthedatawithinaspecifiednumberofstandarddeviationsfromthemean.7.Learnhowtoconstructa5-numbersummaryandaboxplot.8.Beabletocomputeandinterpretcovarianceandcorrelationasmeasuresofassociationbetweentwovariables.9.Beabletocomputeaweightedmean.Chapter33-2Solutions:1.xxni7551510,12,16,17,20Median=16(middlevalue)2.xxni9661610,12,16,17,20,21Median=161716.523.15,20,25,25,27,28,30,3220(8)1.6100i2ndposition=2025(8)2100i202522.5265(8)5.2100i6thposition=2875(8)6100i28302924.Meanxni6571159727.Median=576thitemMode=53Itappears3times5.a.1106.436.8830ixxnb.Thereareanevennumberofitems.Thus,themedianistheaverageofthe15thand16thitemsafterthedatahavebeenplacedinrankorder.Median=36.636.736.652c.Mode=36.4Thisvalueappears4timesDescriptiveStatistics:NumericalMethods3-3d.FirstQuartileiFHGIKJ251003075.Roundingup,weseethatQ1isatthe8thposition.Q1=36.2e.ThirdQuartileiFHGIKJ7510030225.Roundingup,weseethatQ3isatthe23rdposition.Q3=37.96.a.184592.2520ixxnMedianisaverageof10thand11thvaluesafterarranginginascendingorder.6695Median80.52Dataaremultimodalb.133466.720ixxn6670Median682Mode=70(4brokerscharge$70)c.Comparingallthreemeasuresofcentrallocation(mean,medianandmode),weconcludethatitcostsmore,onaverage,totrade500sharesat$50pershare.d.Yes,trading500sharesat$50pershareisatransactionvalueof$25,000whereastrading1000sharesat$5pershareisatransactionvalueof$5000.7.a.xxni13803046b.Yes,themeanhereis46minutes.Thenewspaperreportedonaverageof45minutes.c.Median4552924895..d.Q1=7(valueof8thiteminrankedorder)Q3=70.4(valueof23rditeminrankedlist)Chapter33-4e.Findposition403012;100i40thpercentileisaverageofvaluesin12thand13thpositions.40thpercentile=28.8+29.12=28.958.a.ix=775xxni775203875.Themodalageis29;itappears3times.b.Medianisaverageof10thand11thitems.Median37402385.Datasuggestat-homeworkersareslightlyyounger.c.ForQ1,25205100iSinceiisinteger,1293029.52QForQ3,752015100iSinceiisinteger,3464947.52Qd.32206.4100iSinceiisnotaninteger,werounduptothe7thposition.32ndpercentile=319.a.270,37710,815.0825ixxnMedian(Position13)=8296DescriptiveStatistics:NumericalMethods3-5b.Medianwouldbebetterbecauseoflargedatavalues.c.i=(25/100)25=6.25Q1(Position7)=5984i=(75/100)25=18.75Q3(Position19)=14,330d.i=(85/100)25=21.2585thpercentile(position22)=15,593.Approximately85%ofthewebsiteshavelessthan15,593uniquevisitors.10.a.xi=435xxni43594833.Datainascendingorder:284245484950555860Median=49Donotreportamode;eachdatavalueoccursonce.Theindexcouldbeconsideredgoodsinceboththemeanandmedianarelessthan50.b.2592.25100iQ1(3rdposition)=457596.75100iQ3(7thposition)=5511.52626.320x1516181920212222242426262727303133333458Median=25Donotreportamodesincefivevaluesappeartwice.ForQ1,Chapter33-625205100i1202120.52QForQ3,752015100i3303130.52Q12.Usingthemeanwegetxcity=15.58,xcountry=18.92Forthesamplesweseethatthemeanmileageisbetterinthecountrythaninthecity.City13.214.415.215.315.315.315.91616.116.216.216.716.8MedianMode:15.3Country17.217.418.318.518.618.618.719.019.219.419.420.621.1MedianMode:18.6,19.4Themedianandmodalmileagesarealsobetterinthecountrythaninthecity.13.a.Mean=261/15=17.4141515151616171818181819202121MedianModeis18(occurs4times)Interpretation:theaveragenumberofcredithourstakenwas17.4.Atleast50%ofthestudentstook18ormorehours;atleast50%ofthestudentstook18orfewerhours.Themostfrequentlyoccurringnumberofcredithourstakenwas18.b.ForQ1,DescriptiveStatistics:NumericalMethods3-725153.75100iQ1(4thposition)=15ForQ3,751511.25100iQ3(12thposition)=19c.Forthe70thpercentile,701510.5100iRoundingupweseethe70thpercentileisinposition11.70thpercentile=1814.a.12,780$63920ixxnb.197698.820ixxnpicturesc.2204110.220ixxnminutesd.Thisisnotaneasychoicebecauseitisamulticriteriaproblem.Ifpricewastheonlycriterion,thelowestpricecamera(FujifilmDX-10)wouldbepreferred.Ifmaximumpicturecapacitywastheonlycriterion,themaximumpicturecapacitycamera(KodakDC280Zoom)wouldbepreferred.But,ifbatterylifewastheonlycriterion,themaximumbatterylifecamera(FujifilmDX10)wouldbepreferred.Therearemanyapproachesusedtoselectthebestchoiceinamulticriteriasituation.Theseapproachesarediscussedinmorespecializedbooksondecisionanalysis.15.Range20-10=1010,12,16,17,2025(5)1.25100iQ1(2ndposition)=12Chapter33-875(5)3.75100iQ3(4thposition)=17IQR=Q3-Q1=17-12=516.xxni75515sxxni22164416()s16417.15,20,25,25,27,28,30,34Range=34-15=1925(8)2100i1202522.52Q75(8)6100i1283