Business Statistics A DecisionMaking Approach, 7th …：业务统计决策方法第七… .ppt

businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 1 businessstatistics adecision makingapproach7thedition chapter3describingdatausingnumericalmeasures businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 2 aftercompletingthischapter youshouldbeableto computeandinterpretthemean median andmodeforasetofdatacomputetherange variance andstandarddeviationandknowwhatthesevaluesmeanconstructandinterpretaboxandwhiskergraphcomputeandexplainthecoefficientofvariationandzscoresusenumericalmeasuresalongwithgraphs charts andtablestodescribedata chaptergoals businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 3 chaptertopics measuresofcenterandlocationmean median modeothermeasuresoflocationweightedmean percentiles quartilesmeasuresofvariationrange interquartilerange varianceandstandarddeviation coefficientofvariationusingthemeanandstandarddeviationtogethercoefficientofvariation z scores businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 4 summarymeasures centerandlocation mean median mode othermeasuresoflocation weightedmean describingdatanumerically variation variance standarddeviation coefficientofvariation range percentiles interquartilerange quartiles businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 5 measuresofcenterandlocation centerandlocation mean median mode weightedmean overview businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 6 mean arithmeticaverage themeanisthearithmeticaverageofdatavaluespopulationmeansamplemean n samplesize n populationsize businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 7 mean arithmeticaverage themostcommonmeasureofcentraltendencymean sumofvaluesdividedbythenumberofvaluesaffectedbyextremevalues outliers continued 012345678910 mean 3 012345678910 mean 4 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 8 median inanorderedarray themedianisthe middle number i e thenumberthatsplitsthedistributioninhalfthemedianisnotaffectedbyextremevalues 012345678910 median 3 012345678910 median 3 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 9 median tofindthemedian sortthendatavaluesfromlowtohigh sorteddataiscalledadataarray findthevalueinthei 1 2 npositiontheithpositioniscalledthemedianindexpointifiisnotaninteger rounduptonexthighestinteger continued businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 10 medianexample notethatn 13findthei 1 2 nposition i 1 2 13 6 5since6 5isnotaninteger roundupto7themedianisthevalueinthe7thposition md 12 continued dataarray 4 4 5 5 9 11 12 14 16 19 22 23 24 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 11 shapeofadistribution describeshowdataisdistributedsymmetricorskewed mean median mean median median mean right skewed left skewed symmetric longertailextendstoleft longertailextendstoright businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 12 mode ameasureoflocationthevaluethatoccursmostoftennotaffectedbyextremevaluesusedforeithernumericalorcategoricaldatatheremaybenomodetheremaybeseveralmodes 01234567891011121314 mode 5 0123456 nomode businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 13 weightedmean usedwhenvaluesaregroupedbyfrequencyorrelativeimportance example sampleof26repairprojects weightedmeandaystocomplete businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 14 fivehousesonahillbythebeach reviewexample houseprices 2 000 000500 000300 000100 000100 000 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 15 summarystatistics mean 3 000 000 5 600 000median middlevalueofrankeddata 300 000mode mostfrequentvalue 100 000 houseprices 2 000 000500 000300 000100 000100 000sum3 000 000 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 16 meanisgenerallyused unlessextremevalues outliers existthenmedianisoftenused sincethemedianisnotsensitivetoextremevalues example medianhomepricesmaybereportedforaregion lesssensitivetooutliers whichmeasureoflocationisthe best businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 17 otherlocationmeasures othermeasuresoflocation percentiles quartiles 1stquartile 25thpercentile2ndquartile 50thpercentile median3rdquartile 75thpercentile thepthpercentileinadataarray p arelessthanorequaltothisvalue 100 p aregreaterthanorequaltothisvalue where0 p 100 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 18 percentiles thepthpercentileinanorderedarrayofnvaluesisthevalueinithposition where example findthe60thpercentileinanorderedarrayof19values ifiisnotaninteger rounduptothenexthigherintegervalue sousevalueinthei 12thposition businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 19 quartiles quartilessplittherankeddatainto4equalgroups notethatthesecondquartile the50thpercentile isthemedian 25 25 25 25 q1 q2 q3 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 20 quartiles sampledatainorderedarray 111213161617182122 example findthefirstquartile n 9 q1 25thpercentile sofindi i 9 2 25soroundupandusethevalueinthe3rdposition q1 13 25100 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 21 boxandwhiskerplot agraphicaldisplayofdatausingacentral box andextended whiskers example 25 25 25 25 outlierslower1stmedian3rdupperlimitquartilequartilelimit businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 22 constructingtheboxandwhiskerplot outlierslower1stmedian3rdupperlimitquartilequartilelimit thelowerlimitisq1 1 5 q3 q1 theupperlimitisq3 1 5 q3 q1 thecenterboxextendsfromq1toq3thelinewithintheboxisthemedianthewhiskersextendtothesmallestandlargestvalueswithinthecalculatedlimitsoutliersareplottedoutsidethecalculatedlimits businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 23 shapeofboxandwhiskerplots theboxandcentrallinearecenteredbetweentheendpointsifdataissymmetricaroundthemedian aboxandwhiskerplotcanbeshownineitherverticalorhorizontalformat businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 24 distributionshapeandboxandwhiskerplot right skewed left skewed symmetric q1 q2 q3 q1 q2 q3 q1 q2 q3 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 25 box and whiskerplotexample belowisabox and whiskerplotforthefollowingdata 0222334561127thisdataisrightskewed astheplotdepicts 02361227 minq1q2q3max upperlimit q3 1 5 q3 q1 6 1 5 6 2 12 27isabovetheupperlimitsoisshownasanoutlier businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 26 measuresofvariation variation variance standarddeviation coefficientofvariation populationvariance samplevariance populationstandarddeviation samplestandarddeviation range interquartilerange businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 27 measuresofvariationgiveinformationonthespreadorvariabilityofthedatavalues variation samecenter differentvariation businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 28 range simplestmeasureofvariationdifferencebetweenthelargestandthesmallestobservations range xmaximum xminimum 01234567891011121314 range 14 1 13 example businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 29 ignoresthewayinwhichdataaredistributedsensitivetooutliers 789101112 range 12 7 5 789101112 range 12 7 5 disadvantagesoftherange 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 4 5 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 4 120 range 5 1 4 range 120 1 119 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 30 interquartilerange caneliminatesomeoutlierproblemsbyusingtheinterquartilerangeeliminatesomehigh andlow valuedobservationsandcalculatetherangefromtheremainingvalues interquartilerange 3rdquartile 1stquartile businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 31 interquartilerangeexample median q2 x maximum x minimum q1 q3 example 25 25 25 25 1230455770 interquartilerange 57 30 27 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 32 averageofsquareddeviationsofvaluesfromthemeanpopulationvariance samplevariance variance businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 33 standarddeviation mostcommonlyusedmeasureofvariationshowsvariationaboutthemeanhasthesameunitsastheoriginaldatapopulationstandarddeviation samplestandarddeviation businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 34 calculationexample samplestandarddeviation sampledata xi 1012141517181824 n 8mean x 16 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 35 comparingstandarddeviations mean 15 5s 3 338 1112131415161718192021 1112131415161718192021 datab dataa mean 15 5s 9258 1112131415161718192021 mean 15 5s 4 57 datac samemean butdifferentstandarddeviations businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 36 coefficientofvariation measuresrelativevariationalwaysinpercentage showsvariationrelativetomeanisusedtocomparetwoormoresetsofdatameasuredindifferentunits populationsample businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 37 comparingcoefficientsofvariation stocka averagepricelastyear 50standarddeviation 5stockb averagepricelastyear 100standarddeviation 5 bothstockshavethesamestandarddeviation butstockbislessvariablerelativetoitsprice businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 38 ifthedatadistributionisbell shaped thentheinterval containsabout68 ofthevaluesinthepopulationorthesample theempiricalrule 68 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 39 containsabout95 ofthevaluesinthepopulationorthesamplecontainsabout99 7 ofthevaluesinthepopulationorthesample theempiricalrule 99 7 95 businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 40 regardlessofhowthedataaredistributed atleast 1 1 k2 ofthevalueswillfallwithinkstandarddeviationsofthemeanexamples 1 1 12 0 k 1 1 1 1 22 75 k 2 2 1 1 32 89 k 3 3 tchebysheff stheorem within atleast businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 41 astandardizeddatavaluereferstothenumberofstandarddeviationsavalueisfromthemeanstandardizeddatavaluesaresometimesreferredtoasz scores standardizeddatavalues businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 42 where x originaldatavalue populationmean populationstandarddeviationz standardscore numberofstandarddeviationsxisfrom standardizedpopulationvalues businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 43 where x originaldatavaluex samplemeans samplestandarddeviationz standardscore numberofstandarddeviationsxisfrom standardizedsamplevalues businessstatistics adecision makingapproach 7e 2008prentice hall inc chap3 44 iqscoresinalargepopulationhaveabell shapeddistributionwithmean 100andstandarddeviation 15findthestandardizedscore z score forapersonwithaniqof121 someonewithaniqof121is1 4standarddeviationsabovethemean standardizedvalueexample answer busine