描述数据数值测量章目标金融建模chap003.pptx

描述数据数值测量章目标金融建模chap003.pptx

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DescribingData:

NumericalMeasuresChapter3

3-2GOALSCalculatethearithmeticmean,weightedmean,median,mode,andgeometricmean.Explainthecharacteristics,uses,advantages,anddisadvantagesofeachmeasureoflocation.Identifythepositionofthemean,median,andmodeforbothsymmetricandskeweddistributions.Computeandinterprettherange,meandeviation,variance,andstandarddeviation.Understandthecharacteristics,uses,advantages,anddisadvantagesofeachmeasureofdispersion.UnderstandChebyshev’stheoremandtheEmpiricalRuleastheyrelatetoasetofobservations.

3-3NumericalDescriptiveMeasuresMeasuresofLocationArithmeticMeanWeightedMeanMedianModeGeometricMeanMeasuresofDispersionRangeMeanDeviationVarianceStandardDeviation

3-4PopulationMean Forungroupeddata,thepopulationmeanisthesumofallthepopulationvaluesdividedbythetotalnumberofpopulationvalues:

3-5EXAMPLE–PopulationMean

3-6SampleMeanForungroupeddata,thesamplemeanisthesumofallthesamplevaluesdividedbythenumberofsamplevalues:

3-7EXAMPLE–SampleMean

3-8PropertiesoftheArithmeticMeanEverysetofinterval-levelandratio-leveldatahasamean.Allthevaluesareincludedincomputingthemean.Themeanisunique.Thesumofthedeviationsofeachvaluefromthemeaniszero.

3-9WeightedMeanTheweightedmeanofasetofnumbersX1,X2,...,Xn,withcorrespondingweightsw1,w2,...,wn,iscomputedfromthefollowingformula:

3-10EXAMPLE–WeightedMeanTheCarterConstructionCompanypaysitshourlyemployees$16.50,$19.00,or$25.00perhour.Thereare26hourlyemployees,14ofwhicharepaidatthe$16.50rate,10atthe$19.00rate,and2atthe$25.00rate.Whatisthemeanhourlyratepaidthe26employees?

3-11TheMedianTheMedianisthemidpointofthevaluesaftertheyhavebeenorderedfromthesmallesttothelargest.Thereareasmanyvaluesabovethemedianasbelowitinthedataarray.Foranevensetofvalues,th

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