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Chapter4LandmarkSummaries:InterpretingTypicalValuesandPercentiles,PracticalBusinessStatistics,,ChapterTopics,MeasuresofCentralTendencyMean,Median,ModeMidrange,QuartilesExploratoryDataAnalysisFive-NumberSummaryBoxPlot,,,,,SummaryMeasures,CentralTendency,,Mean,Median,Mode,Midrange,InterquartileRange,Midhinge,,,,,,,,,,,,SummaryMeasures,,,,Variation,,Variance,StandardDeviation,CoefficientofVariation,,,,,Range,,,,,,MeasuresofCentralTendency,,CentralTendency,,Mean,Median,Mode,Midrange,Midhinge,,,,,,,,,,,,,,,,SampleMean,,,,PopulationMean,TheArithmeticAverageofdatavalues:,,TheMean(ArithmeticAverage),,SampleMean,PopulationMean,SampleSize,PopulationSize,,,TheMostCommonMeasureofCentralTendencyAffectedbyExtremeValues(Outliers),,,TheMean(continued),,,012345678910,0123456789101214,,,,,,,,,,,,,Mean=5,Mean=6,,TheMedian,ImportantMeasureofCentralTendencyInanorderedarray,themedianisthe“middle”number.Ifnisodd,themedianisthemiddlenumber.Ifniseven,themedianistheaverageofthe2middlenumbers.,,,TheMedian(continued),,,012345678910,0123456789101214,,,,,,,,,,,,,Median=5,Median=5,NotAffectedbyExtremeValuesForskeweddata,representsthe“typicalcase”betterthantheaveragedoes,,TheMode,,AMeasureofCentralTendencyValuethatOccursMostOftenNotAffectedbyExtremeValues,,,,,,,,,,Mode=8,,,,,,,,012345678910111213,,TheMode(continued),,ThereMayNotbeaModeThereMaybeSeveralModesUsedforEitherNumericalorCategoricalData,,0123456,,,,,,,,NoMode,,0123456,,,,,,,,TwoModes,,,,,,Midrange,,AMeasureofCentralTendencyAverageofSmallestandLargestObservation:,Midrange,,Midrange(continued),,AffectedbyExtremeValue,,,012345678910,012345678910,,,,,,,,,Midrange=5,Midrange=3,,,,,,,Whichsummarytouse?,AverageBestfornormaldataPreservestotalsMedianGoodforskeweddataordatawithoutliers,providedyoudonotneedtopreserveorestimatetotalamountsModeBestforcategories(nominaldata).Themodeistheonlysummarycomputablefornominaldata!,Quartiles,NotameasureofcentraltendencySplitordereddatainto4quarters,,,,,25%,25%,25%,25%,Q1,Q2,Q3,,,SelectedlandmarkstorepresententiredatasetMedian=50thpercentileQuartilesLQ=LowerQuartile=25thpercentileRank=UQ=UpperQuartile=75thpercentileRankisn+1–[rankoflowerquartile]ExtremesSmallest=0thpercentileLargest=100thpercentile,Five-NumberSummary,Five-NumberSummary(continued),ProvidesinformationaboutCentralsummaryRangeofthedata“Middlehalf”ofthedataSkewness,ExploratoryDataAnalysis,BoxPlotGraphicaldisplayofdatausing5-numbersummary,,,,Median(Q2),,,4,6,8,10,12,,,Q,3,,Q,1,,X,largest,,X,smallest,,Spendingrankorderedfromsmallesttolargest0.3,0.6,0.9,1.1,1.4,2.8,3.8,5.512345678LQis(0.6+0.9)/2=0.75UQis(2.8+3.8)/2=3.3,Example:Spending,Example:Spending(continued),Five-numbersummary0.3,0.75,1.25,3.3,5.5BoxplotShowssomeskewness(lackofsymmetry),,,Exercise,,Asystemsmanagerinchargeofacompany’snetworkkeepstrackofthenumberofserverfailuresthatoccurinaday.Thefollowingdatarepresentthenumberofserverfailuresinadayforthepasttwoweeks.30326274023363Obtainthemodeforthesedata,,Solution,,Theorderedarrayforthesedatais:001223333346726Themosttypicalvalue,ormode,is3.Thus,thesystemsmanagercansaythatthemostcommonoccurrenceistohavethreeserverfailuresinaday.Notethatforthisdatasetthemedianisequalto3andthearithmeticmeanisequalto4.5.Thevalue26isanoutlier;thusthemedianandthemodeisabetterdescriptionofcentraltendencythanthemean.,,Exercise,,決策者一旦信奉某種無效的行動方針，常會使自己所犯錯誤逐步升級。組織行為學家和社會心理學家們對這一逐步升級過程產(chǎn)生強烈興趣。諸如“沉沒成本”效應，“陷進泥沼”效應，以及“投入過多，難以自拔”效應，均屬這種現(xiàn)象。不過大多數(shù)人則把此種現(xiàn)象看作是“落入陷阱”。今有52名初學心理學的大學生參加一項實驗室實驗，旨在探究將先出現(xiàn)的結(jié)果視作自我同一性（主觀與客觀的一致性）體現(xiàn)的個人傾向，是否會加強上述落入陷阱效應（AdministrativeScienceQuarterly,May.1986）。整個實驗由30項試驗組成，試驗中根據(jù)學生判斷不同形狀幾何圖形的準確性打分，每項試驗的總得分見表。計算這個數(shù)據(jù)集的平均值、中位數(shù)和眾數(shù)（類）這幾個集中趨勢量度是否出現(xiàn)在數(shù)據(jù)分布的中心？,,Exercise,,54724612111511102342054566155151013946,,Solution,,mean=9.7Median=7Mode=5b.Theanswerisyes,