Applied Statistics in Business and Economics 4E doane Chap004答案.docx
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AppliedStatisticsinBusinessandEconomics4EdoaneChap004答案
Chapter4
DescriptiveStatistics
4.1a.Mean=2.83,Median=1.5,Mode=0.Anyoneofthesewouldbeausefulmeasureofcenter.Dataappearsskewedrightwithmanyvaluesequaltozerosoonemightchoosemedianormodeovermean.
b.Mean=68.33,Median=72,Mode=40.Thisiscontinuousnumericaldatasoeitherthemeanorthemedianwouldbebest.
c.Mean=3.04,Median=3.03,Nomode.Thisiscontinuousnumericaldatasoeitherthemeanorthemedianwouldbebest.
LearningObjective:
04-1
LearningObjective:
04-3
LearningObjective:
04-11
4.2a.Thisisattributedatasomodeistheonlymeasureofcentraltendencypossible.Mode=M,whichoccurs9outof12observations.
b.Thisisdiscretedatawithasmallrangesomodecouldbeanappropriatemeasureofcentraltendency.Mode=18,whichoccurs6outof10observations.
c.Thereisnomodeinthiscasebecausethereisnovaluethatoccursmorethanonce.Therefore,eithermeanormedianwouldbemoreappropriate.Mean=29.5andmedian=29.
LearningObjective:
04-1
LearningObjective:
04-3
LearningObjective:
04-11
4.3a.Continuousdata,skewedright,nomode.Medianisthebestchoice.Median=26.2mpgandmean=28.1mpg.
b.Mostly1riderthereforethemedianorthemodewouldbethebestchoice.Median=mode=1.
c.Symmetricdistribution.Themeanandmedianarethesameandtherearetwomodes.Themeanorthemedianarethebestchoice.Mean=median=3.(Modes=2and4.)
LearningObjective:
04-1
LearningObjective:
04-3
LearningObjective:
04-11
4.4a.Mean=56.22,Median=47,Mode=44.
b.Thedistributionismostlikelyskewedrightbecausethemeanislargerthanthemedianandmode.
c.Themodeisnotausefulmeasureofcentraltendencybecausetherearefewvaluesthatrepeat.Thevalue44appearsonlythreetimesoutof36observations.
LearningObjective:
04-1
LearningObjective:
04-3
LearningObjective:
04-11
4.5a.Mean=75.5,Median=80.5,Mode=93.
b.Thedistributionismostlikelyskewedleftbecausethemeanislessthanthemedianandmode.
c.Themodeisnotausefulmeasureofcentraltendencybecausetherearefewvaluesthatrepeat.Thevalue93appearsonlythreetimesoutof24observations.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
LearningObjective:
04-11
4.6a.
Quiz1
Quiz2
Quiz3
Quiz4
Count
10
10
10
10
Mean
72.00
72.00
76.00
76.00
Median
72.00
72.00
72.00
86.50
Mode
60.00
65.00
72.00
none
Notethatbothquiz2andquiz3havemultiplemodes.Quiz2hasmodesat65and79(4each.)Quiz3hasmodesat72and74(2each.)
b.No,theydon’tagreeforallquizzes.Themeanandthemedianarethesameforquiz1andquiz2,andthemodeandthemedianarethesameforquiz3.
c.Themodeisanunreliablemeasureofcentraltendencyforquantitativedata.Wherethemeanandmediandisagree,oneshouldlookattheshapeofthedistributiontoseewhichmeasureismoreappropriate.
d.Quiz1andQuiz2haveasymmetricdistribution.Eventhoughthemodeisnotequaltothemeanandmedianitissufficienttosaytheyaresymmetricalgiventhatthemeanequalsthemedian.Quiz3isskewedrightbecausethemeanistotherightof(orgreaterthan)themedian.Quiz4isskewedleftbecausethemeanistotheleftof(orlessthan)themedian.
e.Studentsonaveragedidbetteronquizzes3and4.NoneofthestudentsreceivedthesamescoreonQuiz4.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
LearningObjective:
04-11
4.7a.
DescriptiveStatistic
Data
count
32
mean
27.34
mode
26.00
median
26.00
b.Themodeandmedianarethesamevalue,butthemeanisgreaterthanthemedian.
c.
d.Onemightsaydataisslightlyskewedtotherightbecausethemeanisgreaterthanthemedian.Itisdifficulttoconcludeshapebylookingatthegraphs.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
LearningObjective:
04-11
4.8a.
DescriptiveStatistics
Data
count
28
mean
107.25
median
106.00
mode
95.00
b.Themeanandmedianarecloseinvaluebutthemodeismorethan$10lower.
c.
d.Whenlookingatthedotplotonemightsaydataisslightlyskewedtotheright.Thiswouldalsobelogicalbecausethemeanisgreaterthanthemedian.Itisdifficulttoconcludeshapebylookingatthegraphs.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
LearningObjective:
04-11
4.9b.
DescriptiveStatistics
Data
count
65
mean
4.48
median
2.00
mode
1.00
c.No.Themeanismorethantwicethemedianandthemedianistwicethemode.
d.Thedataareskewedtotherightwithafewhighoutliersat20,26,and29minutes.
LearningObjective:
04-1
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04-2
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04-3
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4.10a.Median=68,Midrange=68,GeometricMean=67.37
b.Median=3.03,Midrange=2.96,GeometricMean=3.01
c.Median=1.5,Midrange=7.5,GeometricMeanisundefined.
Themidrangeisnotveryrobustbecauseitissensitivetoextremedatasuchasthe94foroneexamscoreandthe15fornumberofabsences.Themedianandgeometricmeanappeartobecloseinvalueforthefirsttwodatasets.However,wemightwanttorelyonthemedianbecausethedatadonotappeartohaveasteepincreasingtrendandthemedianisamoreeasilyunderstoodandrecognizedmeasureofcentraltendency.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
LearningObjective:
04-11
4.11a.=TRIMMEAN(A1:
A50,0.20)
b.Thereare50observations.Tenpercentof50equalsfive.Sofivevalueswillbedroppedfromeachtail.
c.Iffivevaluesaredroppedfromeachtailthisisatotalof10values.
LearningObjective:
04-2
LearningObjective:
04-3
4.12Excel’sTRIMMEANfunctionmultipliesthetrimmedpercentagebythenumberofobservationsandthentruncatestothenextlowerinteger.ForthefunctionTRIMMEAN(Data,.10)Excelwillmultiplyby.05.
a.Forn=41,.05×41=2.05.Excelwouldtrim2valuesfromeachtail.
b.Forn=66,.05×66=3.3.Excelwouldtrim3valuesfromeachtail.
c.Forn=83,.05×83=4.15.Excelwouldtrim4valuesfromeachtail
LearningObjective:
04-2
LearningObjective:
04-3
4.13a.Mean=100,Median=0,Mode=0,Midrange=325,GeometricMeanisundefinedbecausetherearevaluesequalto0.
b.Choosethemean.Ifplanningforexpectedwork-relatedmedicalexpensesof$100foreightofficersthebudgetshouldbefairlyclose.Usingthemidrangewouldoverestimatetotalexpectedexpensesbyquiteabit.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
LearningObjective:
04-11
4.14a.
Mon
Tue
Wed
Thu
1
1
0
1
1
1
0
1
1
3
0
1
1
3
0
1
5
4
4
1
5
6
6
1
5
6
6
1
6
7
6
1
6
7
6
1
9
9
10
10
b.
DescriptiveStatistics
Mon
Tue
Wed
Thu
mean
4
4.7
3.8
1.9
median
5
5
5
1
mode
1
1
0
1
midrange
5
5
5
5.5
geometricmean
2.89
3.76
NA
1.26
trimmedmean
3.75
4.625
3.5
1
Tuesdayhasmultiplemodesat1,3,6and7andWednesdayhasmultiplemodesat6and0.
c.Thegeometricmeanandmodeareverydifferentfromtheothermeasures.Themean,median,andmidrangearecloseinvalue.
d.Themeanormedianarebettermeasuresofcentraltendencyforthistypeofdata.Themidrangeissensitivetoextremevaluesandignoresmostofthedata.Thegeometricmeanislessfamiliartomostpeopleandthetrimmedmeanmayexcluderelevantdatavalues.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
LearningObjective:
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4.15a.
mean
27.34
midrange
25.50
geometricmean
26.08
trimmean
27.46
b.Themeanandthetrimmedmeanaresimilarinvalueandtheyarebothgreaterthanthemidrangeandthegeometricrange.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
4.16a.
mean
107.25
midrange
114
geometricmean
102.48
trimmedmean
106
b.Themeanandtrimmedmeanaresimilarandfallbetweenthegeometricmeanandmidrange.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
4.17a.
mean
4.48
median
2.00
mode
1.00
midrange
15.00
geometricmean
2.60
trimmedmean
3.13
b.Thedataareskewedtotheright.Themeanisgreaterthanthemedian.Themidrangeismuchgreaterthanthemean.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
04-3
LearningObjective:
04-11
4.187.15%.Seecalculationbelow.
LearningObjective:
04-3
4.19a.
SampleA:
SampleB:
SampleC:
Mean
7
62
1001
SampleStandardDeviation
1
1
1
b.Themidpointofeachsampleisthemean.Theother2datapointsareexactly1standarddeviationfromthemean.Theideaistoillustratethatthestandarddeviationisnotafunctionofthevalueofthemean.
LearningObjective:
04-1
LearningObjective:
04-2
LearningObjective:
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LearningObjective:
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4.20
DataSetA:
DataSetB:
DataSetC:
a.Mean
7.0000
7.0000
7.0000
b.SampleStandardDeviation
1.0000
2.1602
3.8944
c.PopulationStandardDeviation
0.8165
2.0000
3.7417
d.Thesamplestandarddeviationislargerthanthepopulationstandarddeviationforthesamedataset.Thismakessensebecauseintheformulaforsamplestandarddeviation
wedividebyn-1insteadofn.Thisexerciseshowsusthatsamplescanhavesimilarmeans,butdifferentstandarddeviations.Wecannotgetasenseofwhatthestandard
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