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ID:14356073
大小:3.31 MB
页数:24页
时间:2018-07-28
《33 density curves and normal distributions - people :33密度曲线与正态分布的人》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、3.3DensityCurvesandNormalDistributionsDensityCurvesMeasuringCenterandSpreadforDensityCurvesNormalDistributionsThe68-95-99.7RuleStandardizingObservationsUsingtheStandardNormalTableInverseNormalCalculationsNormalQuantilePlots1Wenowhaveakitofgraphicalandnumericaltoolsfordescribingdistribu
2、tions.Wealsohaveastrategyforexploringdataonasinglequantitativevariable.Now,we’lladdonemoresteptothestrategy.ExploringQuantitativeDataAlwaysplotyourdata:Makeagraph.Lookfortheoverallpattern(shape,center,andspread)andforstrikingdeparturessuchasoutliers.Calculateanumericalsummarytobrieflyd
3、escribecenterandspread.Sometimes,theoverallpatternofalargenumberofobservationsissoregularthatwecandescribeitbyasmoothcurve.ExploringQuantitativeData22DensitycurvesAdensitycurveisamathematicalmodelofadistribution…Thetotalareaunderthecurve,bydefinition,isequalto1,or100%.Theareaunderthecu
4、rveforarangeofvaluesistheproportionofallobservationsforthatrange.AreaunderDensityCurve~RelativeFrequencyofHistogramHistogramofasamplewiththesmoothed,densitycurvedescribingtheoreticallythepopulation.rel.freqoflefthistogram=287/947=.303area=.293underrt.curve4Adensitycurveisacurvethat:Isa
5、lwaysonorabovethehorizontalaxisHasanareaofexactly1underneathitAdensitycurvedescribestheoverallpatternofadistribution.Theareaunderthecurveandaboveanyrangeofvaluesonthehorizontalaxisistheproportionofallobservationsthatfallinthatrange.DensityCurvesDensitycurvescomeinmanyshapes.Somearewell
6、knownmathematicallyandothersaren’t–buttheyalllieabovethehorizontalaxisandhavetotalarea=1.6Ourmeasuresofcenterandspreadapplytodensitycurvesaswellastoactualsetsofobservations.Themedianofadensitycurveistheequal-areaspoint―thepointthatdividestheareaunderthecurveinhalf.Themeanofadensitycurv
7、eisthebalancepoint,atwhichthecurvewouldbalanceifmadeofsolidmaterial.Themedianandthemeanarethesameforasymmetricdensitycurve.Theybothlieatthecenterofthecurve.Themeanofaskewedcurveispulledawayfromthemedianinthedirectionofthelongtail.DistinguishingtheMedianandMeanofaDensityCurve6DensityC
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