1Chapter2TheDescriptionofQuantitativeData

定量資料的統計描述2Outline頻數與頻數分布Frequency&Distribution集中趨勢和離散程度Centraltendency&Dispersion統計圖表Table&Graph3PartIDescriptionofQuantitativeDatabyFrequencyTable&Graph4RawData120valuesofheight(cm)for12-year-oldboysin1997:

142.3156.6142.7145.7138.2141.6142.5130.5134.5148.8134.4148.8137.9151.3140.8149.8145.2141.8146.8135.1150.3133.1142.7143.9151.1144.0145.4146.2143.3156.3141.9140.7141.2141.5148.8140.1150.6139.5146.4143.8143.5139.2144.7139.3141.9147.8140.5138.9134.7147.3138.1140.2137.4145.1145.8147.9150.8144.5137.1147.1142.9134.9143.6142.3125.9132.7152.9147.9141.8141.4140.9141.4160.9154.2137.9139.9149.7147.5136.9148.1134.7138.5138.9137.7138.5139.6143.5142.9129.4142.5141.2148.9154.0147.7152.3146.6132.1145.9146.7144.0135.5144.4143.4137.4143.6150.0143.3146.5149.0142.1140.2145.4142.4148.9146.7139.2139.6142.4138.7139.95ClassIntervalforHeight(cm)Frequency(f)RelativeFrequency124~128~132~136~140~144~148~152~156~160~TotalFrequencytableforQuantitativeData1210223726154211200.00830.01670.08330.18340.30830.21670.12500.03330.01670.00831.00006124132140148156164010203040Thefrequencydistributionoftheheightsof12012-year-oldboys

FrequencyHistogramforQuantitativeData高峰位于中間，兩側基本對稱NormalDistributionVeryusefulinformationforthefinalanalysis7FrequencytableforcategoricaldataBloodTypeFreq.RelativeFreq.(%)O20540.43A11222.09B15029.59AB407.89TOTAL507100.008PartIIDescriptionofQuantitativeDatabyStatisticsMeasuresofCentralTendency&Dispersion9Centraltendency：Average

集中趨勢：平均數算數均數Arithmeticmean幾何均數Geometricmean中位數和百分位數Median&Percentiles眾數Mode10ArithmeticMean,MeanThemostwidelyutilizedmeasureoflocationpopulationmean:μsamplemean:aletterwithabaroveritPreferredwhenthedataare“symmetrywithsinglepeak”.11AnExampleAsmallpopulationconsistsof10boysTheheights(cm)are:13616015514213815214814014516112If5ofthe10boysweresampledrandomlyandwewanttocalculatethesamplemean13614213814814513weightedmean

Meanisaspecialcaseofweightedmean14Geometricmean:

15ExampleforGeometricmeantitrevalueoffiveantibody1:10,1:20,1:40,1:80,1:16016MedianMiddlevalueinrankedlist.HalfofthevaluesfallaboveandhalffallbelowAdvantage:Lessaffectedbyextremes;Drawback:Wastefulofinformation.Preferablewhendataarenotsymmetric17ExamplesforMedianvaluesofHg(hydrargyrum)ofhair1.1,1.83.54.24.85.65.97.110.5

M=4.81.1,1.83.54.24.85.65.97.1>16

M=4.81.1,1.83.54.24.85.65.97.110.5>16

M=(4.8+5.6)/2=5.2

18ModeThemodeisdefinedasthemostfrequentlyoccurringvalueinthedataset.Eample:4556148952Themodeis519Whichmeasureshouldweuse?Mean:

symmetric,unimodal;G:

iflogtransformationcreatessymmetric,unimodal;Mode:unimodal;M:distributionfree.uncertaindataThesubjectsshouldbehomogeneitywhenwecalculateaverage!20IthasbeensaidthatafellowwithonelegfrozeniniceandtheotherleginboilingwateriscomfortableONAVERAGE!21真實的笑料：國家統計局不會計算平均數!?國家統計局人口就業司司長馮乃林表示，工資“被增長”是一種誤解，在金融危機中，處于工資低端的崗位和企業減少，而處于工資高端的崗位和企業變化較小，是造成平均工資數據仍然上升的原因之一。國家統計局承認因統計面過窄致使平均工資被增長國家統計局2009年7月29日表示，上半年，中國城鎮單位在崗職工平均工資為14638元，同比增長12.9%，有網民稱，統計數據與自己的收入不符。222012年1月21日國家統計局首次公布了城鄉居民收入的中位數報告顯示，2011年城鎮居民人均可支配收入中位數為19118元，此前公布的數據中，城鎮居民人均可支配收入平均數比中位數高2692元。在過去，居民收入數據一公布，很多人就會說自己又“被增長”了。其實，數字并沒有水分，“被增長”原因之一是“平均數”，就現實國情而言，國內收入結構并非理想的中產占多數的橄欖型，“削峰平谷”的“平均數”其實變相掩蓋了收入差異，比例較高的中低收入者自然不會買賬。23MeasuresofdispersionGroupA：2628303234GroupB：2427303336GroupC：242930313424Rangerange

R=max－minAdvantage:Easytocalculate.Drawback:Unstable,notsensitive.

25ExampleGroupA：2628303234GroupB：2427303336GroupC：2629303134Theirrangeare8,12and8respectively.However,GroupAandChavedifferentdegreeofdispersion26inter-quartilerange

QU－QL＝

P75－P25

27VarianceApopulationvarianceisdenotedbyσ2,Asamplevarianceisdenotedbys2,28Standarddeviation(SD)Apopulationsdisdenotedbyσ,Asamplesdisdenotedbys,29Example:A:2628303234B:2427303336C:2629303134rangevariancesdmeanGroupA:8 10.0 3.1630GroupB:12 22.5 4.7430GroupC:8 8.5 2.9230

30CoefficientofVariationcoefficientofvariation,CVnonzeromean.Makecomparisonbetweendifferentdistributions.forvariableswithdifferentscaleorunit;forvariableswithmoredifferentmeans.31Example:Comparingthedispersionoftwovariables

mean sdHeight: 166.06(cm) 4.95(cm)Weight: 53.72(kg)