101
PublisherB
#ofbooks
Freq.
Rel.Freq.
0
18
1
24
2
24
3
22
4
15
5
10
7
5
9
1
Table2.19
PublisherC
#ofbooks
Freq.
Rel.Freq.
0-1
20
2-3
35
4-5
12
6-7
2
8-9
1
Table2.20
a. Findtherelativefrequenciesforeachsurvey.Writetheminthecharts.
b. Usingeitheragraphingcalculator,computer,orbyhand,usethefrequencycolumntoconstruct
ahistogramforeachpublisher’ssurvey.ForPublishersAandB,makebarwidthsof1. For
PublisherC,makebarwidthsof2.
c. Incompletesentences,givetworeasonswhythegraphsforPublishersAandBarenotidentical.
d. WouldyouhaveexpectedthegraphforPublisherCtolookliketheothertwographs?Whyor
whynot?
e. MakenewhistogramsforPublisherAandPublisherB.Thistime,makebarwidthsof2.
f. Now,comparethegraphforPublisherCtothenewgraphsforPublishersAandB.Arethe
graphsmoresimilarormoredifferent?Explainyouranswer.
Exercise2.13.14
Often,cruiseshipsconductallon-boardtransactions,withtheexceptionofgambling,onacash-
lessbasis.Attheendofthecruise,guestspayonebillthatcoversallon-boardtransactions.Sup-
posethat60singletravelersand70couplesweresurveyedastotheiron-boardbillsforaseven-day
cruisefromLosAngelestotheMexicanRiviera.Belowisasummaryofthebillsforeachgroup.
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102
CHAPTER2. DESCRIPTIVESTATISTICS
Singles
Amount($)
Frequency
Rel.Frequency
51-100
5
101-150
10
151-200
15
201-250
15
251-300
10
301-350
5
Table2.21
Couples
Amount($)
Frequency
Rel.Frequency
100-150
5
201-250
5
251-300
5
301-350
5
351-400
10
401-450
10
451-500
10
501-550
10
551-600
5
601-650
5
Table2.22
a. Fillintherelativefrequencyforeachgroup.
b. Constructahistogramfor theSinglesgroup. . Scalethex-axisby$50. . widths. Userelative
frequencyonthey-axis.
c. ConstructahistogramfortheCouplesgroup.Scalethex-axisby$50.Userelativefrequencyon
they-axis.
d. Comparethetwographs:
i. Listtwosimilaritiesbetweenthegraphs.
ii. Listtwodifferencesbetweenthegraphs.
iii. Overall,arethegraphsmoresimilarordifferent?
e. Constructanewgraphforthe Couplesbyhand. . Sinceeachcouple e ispayingfortwoindi-
viduals,insteadofscalingthex-axisby$50,scaleitby$100. Userelativefrequencyonthe
y-axis.
f. ComparethegraphfortheSingleswiththenewgraphfortheCouples:
i. Listtwosimilaritiesbetweenthegraphs.
ii. Overall,arethegraphsmoresimilarordifferent?
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103
i. ByscalingtheCouplesgraphdifferently,howdiditchangethewayyoucomparedittothe
Singles?
j. Basedonthegraphs,doyouthinkthatindividualsspendthesameamount,moreorless,as
singlesastheydopersonbypersoninacouple? Explainwhyinoneortwocompletesen-
tences.
Exercise2.13.15
(Solutiononp.118.)
Refertothefollowinghistogramsandboxplot. Determinewhichofthefollowingaretrueand
whicharefalse.Explainyoursolutiontoeachpartincompletesentences.
a. Themediansforallthreegraphsarethesame.
b. Wecannotdetermineifanyofthemeansforthethreegraphsisdifferent.
c. Thestandarddeviationfor(b)islargerthanthestandarddeviationfor(a).
d. Wecannotdetermineifanyofthethirdquartilesforthethreegraphsisdifferent.
Exercise2.13.16
Refertothefollowingboxplots.
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104
CHAPTER2. DESCRIPTIVESTATISTICS
a. Incompletesentences,explainwhyeachstatementisfalse.
i. Data1hasmoredatavaluesabove2thanData2hasabove2.
ii. Thedatasetscannothavethesamemode.
iii. ForData1,therearemoredatavaluesbelow4thanthereareabove4.
b. Forwhichgroup,Data1orData2,isthevalueof“7”morelikelytobeanoutlier?Explainwhy
incompletesentences
Exercise2.13.17
(Solutiononp.119.)
InarecentissueoftheIEEESpectrum,84engineeringconferenceswereannounced. Fourcon-
ferenceslastedtwodays.Thirty-sixlastedthreedays.Eighteenlastedfourdays.Nineteenlasted
fivedays. Fourlastedsixdays. . Onelastedsevendays. Onelastedeightdays. Onelastednine
days.LetX=thelength(indays)ofanengineeringconference.
a. Organizethedatainachart.
b. Findthemedian,thefirstquartile,andthethirdquartile.
c. Findthe65thpercentile.
d. Findthe10thpercentile.
e. Constructaboxplotofthedata.
f. Themiddle50%oftheconferenceslastfrom_______daysto_______days.
g. Calculatethesamplemeanofdaysofengineeringconferences.
h. Calculatethesamplestandarddeviationofdaysofengineeringconferences.
i. Findthemode.
j. Ifyouwereplanninganengineeringconference,whichwouldyouchooseasthelengthofthe
conference:mean;median;ormode?Explainwhyyoumadethatchoice.
k. Givetworeasonswhyyouthinkthat3-5daysseemto bepopularlengthsofengineering
conferences.
Exercise2.13.18
Asurveyofenrollmentat35communitycollegesacrosstheUnitedStatesyieldedthefollowing
figures(source:MicrosoftBookshelf):
6414; 1550; 2109; 9350;21828;4300;5944;5722; 2825; 2044; 5481;5200;5853; 2750; 10012; 6357;
27000;9414;7681;3200;17500;9200;7380;18314;6557;13713;17768;7493;2771;2861;1263;7285;
28165;5080;11622
a. Organizethedataintoachartwithfiveintervalsofequalwidth. Labelthetwocolumns"En-
rollment"and"Frequency."
b. Constructahistogramofthedata.
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105
c. Ifyouwereto buildanewcommunitycollege, whichpiece ofinformationwouldbemore
valuable:themodeorthemean?
d. Calculatethesamplemean.
e. Calculatethesamplestandarddeviation.
f. Aschoolwithanenrollmentof8000wouldbehowmanystandarddeviationsawayfromthe
mean?
Exercise2.13.19
(Solutiononp.119.)
ThemedianageoftheU.S.populationin1980was30.0years. In1991,themedianagewas33.1
years.(Source:BureauoftheCensus)
a. Whatdoesitmeanforthemedianagetorise?
b. Givetworeasonswhythemedianagecouldrise.
c. Forthemedianagetorise,istheactualnumberofchildrenlessin1991thanitwasin1980?
Whyorwhynot?
Exercise2.13.20
Asurveywasconductedof130purchasersofnewBMW3seriescars,130purchasersofnew
BMW5seriescars,and130purchasersofnewBMW7seriescars.Init,peoplewereaskedtheage
theywerewhentheypurchasedtheircar.Thefollowingboxplotsdisplaytheresults.
a. Incompletesentences,describewhattheshapeofeachboxplotimpliesaboutthedistribution
ofthedatacollectedforthatcarseries.
b. Whichgroupismostlikelytohaveanoutlier?Explainhowyoudeterminedthat.
c. Comparethethreeboxplots.WhatdotheyimplyabouttheageofpurchasingaBMWfromthe
serieswhencomparedtoeachother?
d. LookattheBMW5series.Whichquarterhasthesmallestspreadofdata?Whatisthatspread?
e. LookattheBMW5series.Whichquarterhasthelargestspreadofdata?Whatisthatspread?
f. LookattheBMW5series.EstimatetheInterQuartileRange(IQR).
g. LookattheBMW5series. Aretheremoredataintheinterval31-38orintheinterval45-55?
Howdoyouknowthis?
h. LookattheBMW5series.Whichintervalhasthefewestdatainit?Howdoyouknowthis?
i. 31-35
ii. 38-41
iii. 41-64
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106
CHAPTER2. DESCRIPTIVESTATISTICS
Exercise2.13.21
(Solutiononp.119.)
The followingboxplotshowsthe U.S.populationfor1990,the latest availableyear. . (Source:
BureauoftheCensus,1990Census)
a. Aretherefewerormorechildren(age17andunder)thanseniorcitizens(age65andover)?
Howdoyouknow?
b. 12.6%areage65andover. Approximatelywhatpercentofthepopulationareofworkingage
adults(aboveage17toage65)?
Exercise2.13.22
JavierandErciliaaresupervisorsatashoppingmall.Eachwasgiventhetaskofestimatingthe
meandistancethatshopperslivefromthemall.Theyeachrandomlysurveyed100shoppers.The
samplesyieldedthefollowinginformation:
Javier
Ercilla
x
6.0miles
6.0miles
s
4.0miles
7.0miles
Table2.23
a. Howcanyoudeterminewhichsurveywascorrect?
b. Explainwhatthedifferenceintheresultsofthesurveysimpliesaboutthedata.
c. Ifthetwohistogramsdepictthedistributionofvaluesforeachsupervisor,whichonedepicts
Ercilia’ssample?Howdoyouknow?
Figure2.2
d. Ifthetwoboxplotsdepictthedistributionofvaluesforeachsupervisor,whichonedepicts
Ercilia’ssample?Howdoyouknow?
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107
Figure2.3
Exercise2.13.23
(Solutiononp.119.)
Studentgradesonachemistryexamwere:
77,78,76,81,86,51,79,82,84,99
a. Constructastem-and-leafplotofthedata.
b. Arethereanypotentialoutliers? Ifso, , whichscoresarethey? ? Whydo o youconsiderthem
outliers?
2.13.1Trythesemultiplechoicequestions(Exercises24-30).
Thenextthreequestionsrefertothefollowinginformation. Weareinterestedinthenumberofyears
studentsinaparticularelementarystatisticsclasshavelivedinCalifornia.Theinformationinthefollowing
tableisfromtheentiresection.
Numberofyears
Frequency
7
1
14
3
15
1
18
1
19
4
20
3
22
1
23
1
26
1
40
2
42
2
Total=20
Table2.24
Exercise2.13.24
(Solutiononp.119.)
WhatistheIQR?
A. 8
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108
CHAPTER2. DESCRIPTIVESTATISTICS
B. 11
C. 15
D. 35
Exercise2.13.25
(Solutiononp.119.)
Whatisthemode?
A. 19
B. 19.5
C. 14and20
D. 22.65
Exercise2.13.26
(Solutiononp.119.)
Isthisasampleortheentirepopulation?
A. sample
B. entirepopulation
C. neither
Thenexttwoquestionsrefertothefollowingtable.X=thenumberofdaysperweekthat100clientsuse
aparticularexercisefacility.
x
Frequency
0
3
1
12
2
33
3
28
4
11
5
9
6
4
Table2.25
Exercise2.13.27
(Solutiononp.119.)
The80thpercentileis:
A. 5
B. 80
C. 3
D. 4
Exercise2.13.28
(Solutiononp.119.)
Thenumberthatis1.5standarddeviationsBELOWthemeanisapproximately:
A. 0.7
B. 4.8
C. -2.8
D. Cannotbedetermined
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109
Thenexttwoquestionsrefer tothefollowinghistogram. Suppose onehundred eleven n people e who
shoppedinaspecialT-shirtstorewereaskedthenumberofT-shirtstheyowncostingmorethan$19each.
Exercise2.13.29
(Solutiononp.119.)
Thepercentofpeoplethatownatmostthree(3)T-shirtscostingmorethan$19eachisapproxi-
mately:
A. 21
B. 59
C. 41
D. Cannotbedetermined
Exercise2.13.30
(Solutiononp.119.)
Ifthedatawerecollectedbyaskingthefirst111peoplewhoenteredthestore,thenthetypeof
samplingis:
A. cluster
B. simplerandom
C. stratified
D. convenience
Exercise2.13.31
(Solutiononp.119.)
Below are e the 2010 obesity rates by U.S. states s and Washington, , DC.(Source:
http://www.cdc.gov/obesity/data/adult.html))
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110
CHAPTER2. DESCRIPTIVESTATISTICS
State
Percent(%)
State
Percent(%)
Alabama
32.2
Montana
23.0
Alaska
24.5
Nebraska
26.9
Arizona
24.3
Nevada
22.4
Arkansas
30.1
NewHampshire
25.0
California
24.0
NewJersey
23.8
Colorado
21.0
NewMexico
25.1
Connecticut
22.5
NewYork
23.9
Delaware
28.0
NorthCarolina
27.8
Washington,DC
22.2
NorthDakota
27.2
Florida
26.6
Ohio
29.2
Georgia
29.6
Oklahoma
30.4
Hawaii
22.7
Oregon
26.8
Idaho
26.5
Pennsylvania
28.6
Illinois
28.2
RhodeIsland
25.5
Indiana
29.6
SouthCarolina
31.5
Iowa
28.4
SouthDakota
27.3
Kansas
29.4
Tennessee
30.8
Kentucky
31.3
Texas
31.0
Louisiana
31.0
Utah
22.5
Maine
26.8
Vermont
23.2
Maryland
27.1
Virginia
26.0
Massachusetts
23.0
Washington
25.5
Michigan
30.9
WestVirginia
32.5
Minnesota
24.8
Wisconsin
26.3
Mississippi
34.0
Wyoming
25.1
Missouri
30.5
Table2.26
a.. Constructabargraphofobesityratesofyourstateandthefourstatesclosesttoyourstate.
Hint:Labelthex-axiswiththestates.
b.. Usearandomnumbergeneratortorandomlypick8states.Constructabargraphoftheobesity
ratesofthose8states.
c.. Constructabargraphforallthestatesbeginningwiththeletter"A."
d.. Constructabargraphforallthestatesbeginningwiththeletter"M."
Exercise2.13.32
(Solutiononp.120.)
Amusicschoolhasbudgetedtopurchase3musicalinstruments.Theyplantopurchaseapiano
costing$3000,aguitarcosting$550,andadrumsetcosting$600. Themeancostforapianois
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