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+1rankoflowerquartileExtremesSmallest=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,Asystemsmanagerinchargeofacompanysnetworkkeepstrackofthenumberofserverfailuresthatoccurinaday.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(xué)家和社會心理學(xué)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(yīng)，“陷進(jìn)泥沼”效應(yīng)，以及“投入過多，難以自拔”效應(yīng)，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(xué)心理學(xué)的大學(xué)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(yīng)（AdministrativeScienceQuarterly,May.1986）。整個實驗由30項試驗組成，試驗中根據(jù)學(xué)生判斷不同形狀幾何圖形的準(zhǔn)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,