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33 density curves and normal distributions - people ：33密度曲线与正态分布的人

33 density curves and normal distributions - people ：33密度曲线与正态分布的人

ID：14356073

大小：3.31 MB

页数：24页

时间：2018-07-28

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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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