Chapter 02 A city in the Pacific Northwest recorded its

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Ch.2 DescriptiveStatistics

2.1 FrequencyDistributionsandTheirGraphs

1 InterpretaFrequencyDistribution

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usethegivenfrequencydistributiontofindthe

(a)classwidth.

(b)classmidpointsofthefirstclass.

(c)classboundariesofthefirstclass.

1) Height(ininches)

Class Frequency,f

50–52 5

53–55 8

56–58 12

59–61 13

62–64 11

A) (a)3

(b)51

(c)49.5–52.5

B) (a)2

(b)51.5

(c)49.5–52.5

C) (a)3

(b)51

(c)50–52

D) (a)2

(b)51.5

(c)50–52

2) PhoneCalls(perday)

Class Frequency,f

8–11 18

12–15 23

16–19 38

20–23 47

24–27 32

A) (a)4

(b)9.5

(c)7.5–11.5

B) (a)3

(b)10.5

(c)8–11

C) (a)4

(b)10.5

(c)8–11

D) (a)3

(b)9.5

(c)7.5–11.5

3) Weight(inpounds)

Class Frequency,f

135–139 6

140–144 4

145–149 11

150–154 15

155–159 8

A) (a)5

(b)137

(c)134.5–139.5

B) (a)5

(b)137

(c)135–139

C) (a)4

(b)137.5

(c)134.5–139.5

D) (a)4

(b)137.5

(c)135–139

Page9

4) Miles(perday)

Class Frequency,f

1–29

3–422

5–628

7–815

9–10 4

A) (a)2

(b)1.5

(c)0.5–2.5

B) (a)1

(b)1.5

(c)0.5–2.5

C) (a)2

(b)1

(c)1–2

D) (a)1

(b)1

(c)1–2

2 InterpretFrequencyDistributionGraphs

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Usethegivenfrequencydistributiontoconstructafrequencyhistogram,arelativefrequencyhistogramandafrequency

polygon.

1) Height(ininches)

Class Frequency,f

50–52 5

53–55 8

56–58 12

59–61 13

62–64 11

2) Weight(inpounds)

Class Frequency,f

135–139 6

140–144 4

145–149 11

150–154 15

155–159 8

Usethegivenfrequencydistributiontoconstructacumulativefrequencydistributionandanogive.

3) PhoneCalls(perday)

Class Frequency,f

8–11 18

12–15 23

16–19 38

20–23 47

24–27 32

4) Height(ininches)

Class Frequency,f

50–52 5

53–55 8

56–58 12

59–61 13

62–64 11

Page10

5) Weight(inpounds)

Class Frequency,f

135–139 6

140–144 4

145–149 11

150–154 15

155–159 8

6) Miles(perday)

Class Frequency,f

1–29

3–422

5–628

7–815

9–10 4

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

7) Usetheogivebelowtoapproximatethenumberinthesample.

A) 80 B) 100 C) 341 D) 28

8) Usetheogivebelowtoapproximatethecumulativefrequencyfor24hours.

A) 63 B) 17 C) 27 D) 75

Page11

3 ConstructaFrequencyDistributionfromDataSet

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) AcityinthePacificNorthwestrecordeditshighesttemperatureat89 degreesFahrenheitanditslowest

temperatureat28degreesFahrenheitforaparticularyear.Usethisinformationtofindtheupperandlower

limitsofthefirstclassifyouwishtoconstructafrequencydistributionwith10classes.

A) 28–34 B) 28–35 C) 23–33 D) 28–33

2) Asampleofcandieshaveweightsthatvaryfrom2.35gramsto4.75grams.Usethisinformationtofindthe

upperandlowerlimitsofthefirstclassifyouwishtoconstructafrequencydistributionwith12classes.

A) 2.35–2.55 B) 2.35–2.54 C) 2.35–2.65 D) 2.35–2.75

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Thegradepointaveragesfor40studentsarelistedbelow.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

3.1 2.4 2.4 2.3 1.6 1.6 4.0 3.1 3.2 1.8

2.2 2.2 1.7 0.5 3.6 3.4 1.9 2.0 3.0 1.1

3.0 4.0 4.0 2.1 1.9 1.1 0.5 3.2 3.0 2.2

3) Constructafrequencydistribution,arelativefrequencydistribution,andacumulativefrequencydistribution

usingeightclasses.Includethemidpointsoftheclasses.

4) Constructafrequencyhistogram,arelativefrequencyhistogramandafrequencypolygonusingeightclasses.

5) Constructanogiveusingeightclasses.

Theheights(ininches)of30adultmalesarelistedbelow.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

69 71 68 67 73 74 70 71 69 68

6) Constructafrequencydistribution,arelativefrequencydistribution,andacumulativefrequencydistribution

usingfiveclasses.

7) Constructafrequencyhistogramusingfiveclasses.

8) Constructarelativefrequencyhistogramusingfiveclasses.

9) Constructafrequencypolygonusingfiveclasses.

10) Constructaogiveusingfiveclasses.

Page12

TheHighwayPatrol,usingradar,checkedthespeeds(inmph)of30passingmotoristsatacheckpoint.Theresultsare

listedbelow.

44 38 41 50 36 36 43 42 49 48

35 40 37 41 43 50 45 45 39 38

50 41 47 36 35 40 42 43 48 33



11) Constructafrequencydistribution,arelativefrequencydistribution,andacumulativefrequencydistribution

usingsixclasses.

12) Constructafrequencyhistogram,arelativefrequencyhistogramandafrequencypolygonusingsixclasses.

13) Constructanogiveusingsixclasses.

Provideanappropriateresponse.

14) ListedbelowaretheACTscoresof40randomlyselectedstudentsatamajoruniversity.

18 22 13 15 24 24 20 19 19 12

16 25 14 19 21 23 25 18 18 13

26 26 25 25 19 17 18 15 13 21

19 19 14 24 20 21 23 22 19 17

a)Constructarelativefrequencyhistogramofthedata,usingeightclasses.

b)Iftheuniversitywantstoacceptthetop90%oftheapplicants,whatshouldtheminimumscorebe?

c)Iftheuniversitysetstheminimumscoreat17,whatpercentoftheapplicantswillbeaccepted?

4 Concepts

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Explainthedifferencebetweenclasslimitsandclassboundaries.

2.2 MoreGraphsandDisplays

1 InterpretDataSets

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) ThenumbersofhomerunsthatSammySosahitinthefirst15yearsofhismajorleaguebaseballcareerare

listedbelow.Makeastem–and–leafplotforthisdata.Whatcanyouconcludeaboutthedata?

415 10 833 25 36 40 36 66 63 50 64 49 40

2) ThenumbersofhomerunsthatBarryBondshitinthefirst18yearsofhismajorleaguebaseballcareerare

listedbelow.Makeastem–and–leafplotforthisdata.Whatcanyouconcludeaboutthedata?

16 25 24 19 33 25 34 46 37

33 42 40 37 34 49 73 46 45

Page13

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

3) Forthestem–and–leafplotbelow,whatisthemaximumandwhatistheminimumentry?

Key:11 7=11.7

67

466789

0112366788

34668999

011237789

22578899

03

A) max:17.3;min:11.6 B) max:173;min:116

C) max:17.0;min:11.6 D) max:17.3;min:11.7

4) Forthedotplotbelow,whatisthemaximumandwhatistheminimumentry?

A) max:17;min:12 B) max:54;min:15 C) max:54;min:12 D) max:14;min:12

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

5) Theheights(ininches)of30adultmalesarelistedbelow.Constructastem–and–leafchartforthedata.

Whatcanyouconcludeaboutthedata?

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

69 71 68 67 73 74 70 71 69 68

6) TheHighwayPatrol,usingradar,checkedthespeeds(inmph)of30passingmotoristsatacheckpoint.The

resultsarelistedbelow.Constructastem–and–leafplotforthedata,listingeachstemtwice.Whatcanyou

concludeaboutthedata?

44 38 41 50 36 36 43 42 49 48

35 40 37 41 43 50 45 45 39 38

50 41 47 36 35 40 42 43 48 33

Page14

2 GraphDataSets

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) TheHighwayPatrol,usingradar,checkedthespeeds(inmph)of30passingmotoristsatacheckpoint.The

resultsarelistedbelow.Constructadotplotforthedata.

44 38 41 50 36 36 43 42 49 48

35 40 37 41 43 50 45 45 39 38

50 41 47 36 35 40 42 43 48 33

2) Theheights(ininches)of30adultmalesarelistedbelow.Constructadotplotforthedata.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

69 71 68 67 73 74 70 71 69 68

3) Astudywasconductedtodeterminehowpeoplegetjobs.Fourhundredsubjectswererandomlyselectedand

theresultsarelistedbelow.

JobSourcesof

SurveyRespondents Frequency

Newspaperwantads 69

Onlineservices 124

Executivesearchfirms 72

Mailings 32

Networking 103

Constructapiechartofthedata.

4) Astudywasconductedtodeterminehowpeoplegetjobs.Fourhundredsubjectswererandomlyselectedand

theresultsarelistedbelow.

JobSourcesof

SurveyRespondents Frequency

Newspaperwantads 72

Onlineservices 124

Executivesearchfirms 69

Mailings 32

Networking 103

ConstructaParetochartofthedata.

5) Theheights(ininches)of30adultmalesarelistedbelow.ConstructaParetochartforthedata.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

69 71 68 67 73 74 70 71 69 68

Page15

6) Useascatterplottodisplaythedatabelow.Allmeasurementsareinmilligramspercigarette.

Brand Tar Nicotine

Benson&Hedges 16 1.2

LuckyStrike 13 1.1

Marlboro 16 1.2

Viceroy 18 1.4

True 6 0.6

7) ThenumbersofhomerunsthatBarryBondshitinthefirst10yearsofhismajorleaguebaseballcareerare

listedbelow.Useascatterplottodisplaythedata.Istherearelationshipbetweenthehomerunsandthe

battingaverages?

HomeRuns

BattingAverage

16 25 24 19 33 25 34 46 37 33

.223 .261 .283 .248 .301 .292 .311 .336 .312 .294

8) Thedatabelowrepresentthenumbersofabsencesandthefinalgradesof15randomlyselectedstudentsfroma

statisticsclass.Useascatterplottodisplaythedata.Istherearelationshipbetweenthestudentsʹabsencesand

theirfinalgrades?

Student NumberofAbsences FinalGradeasaPercent

15 79

26 78

32 86

412 56

59 75

65 90

78 78

815 48

90 92

10 1 78

11 9 81

12 3 86

13 10 75

14 3 89

15 11 65

9) Thedatabelowrepresenttheinfantmortalityratesandthelifeexpectanciesforsevenselectedcountriesin

Africa.Useascatterplottodisplaythedata.

InfantMortality 63 199 71 61 67 35 194

LifeExpectancy 45 31 51 47 39 70 37

10) ThedatabelowrepresentthesmokingprevalenceamongU.S.adultsovera35 –yearperiod.Useatimeseries

charttodisplaythedata.Describeanytrendsshown.

Year 1965 1985 1990 1995 2000

PercentofSmokers 42 30 25 25 23

Page16

11) Asafetyengineerwishestousethefollowingdatatoshowthenumberofdeathsfromthecollisionof

passengercarswithtrucksonaparticularhighway.Useatimeseriescharttodisplaythedata.Describeany

trendsshown.

Year NumberofDeaths

1930 12

1940 17

1950 22

1960 21

1970 16

1980 13

1990 11

2000 12

12) WomenwereallowedtoentertheBostonMarathonforthefirsttimein1972.Listedbelowarethewinning

womenʹstimes(inminutes)forthefirst10years.Useatimeseriescharttodisplaythedata.

Year

Time

1972 1973 1974 1975 1976 1977 1978 1979 1980 1981

190 186 167 162 167 168 165 155 154 147

13) ThefivelongestwinningstreaksforNCAAMenʹsDivisionIBasketballarelistedbelow.ConstructaPareto

chartforthedata.

University NumberofGames

Indiana 57

SanFrancisco 51

UCLA 76

Marquette 56

Kentucky 54

14) Thelengths,inkilometers,oftheworldʹslargestsubwaysystemsarelistedbelow.ConstructaParetochartfor

thedata.

City Length

Moscow 340

Paris 211

London 415

Tokyo 281

NewYorkCity 371

15) Thenumberofbedsinasampleof24hospitalsarelistedbelow.Constructastem –and–leafplotforthedata.

149 167 162 127 130 180 160 167

221 145 137 194 207 150 254 262

244 287 137 204 166 174 180 151

Page17

16) Thenumberofminutesthatadentistkept20patientswaitingbeyondtheirappointmenttimesarelistedbelow.

Constructastem–and–leafplotforthedata.

12.9 12.1 9.6 9.8 11.5 13.0 10.5 10.3 15.7 11.3

10.7 10.0 13.0 9.7 11.4 12.8 11.9 9.3 9.6 10.1

17) Astudywasconductedtodeterminehowcertainfamiliespayontheircreditcardbalances.Twohundred

familieswithahouseholdannualincomebetween$25,000and$49,999wererandomlyselectedandtheresults

arelistedbelow.Constructapiechartofthedata.

Paymentschedule Frequency

Almostalwayspayoffbalance 97

Sometimespayoffbalance 41

Hardlyeverpayoffbalance 62

18) Ofthe55tornadofatalitiesinarecentyear,thelocationsofthevictimsarelistedbelow.Constructapiechart

ofthedata.

Location Fatalities

Mobilehome 37

Permanenthome 10

Vehicle 4

Business 2

Unknown 2

19) Thedatabelowrepresentthealcohol–relateddrivingfatalities,inthousands,intheUnitedStatesovera

20–yearperiod.Useatimeseriescharttodisplaythedata.Describeanytrendsshown.

Year 1983 1985 1987 1989 1991 1993 1995 1997 19992001

Fatalities 25 23 24 22 20 18 18 17 1717

2.3 MeasuresofCentralTendency

1 InterprettheGraphofaDistribution

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Forthegivendata,constructafrequencydistributionandfrequencyhistogramofthedatausingfiveclasses.Describe

theshapeofthehistogramassymmetric,uniform,skewedleft,orskewedright.

1) Dataset:CaliforniaPickThreeLottery

3676061784

1575915399

2230884024

A) uniform B) symmetric C) skewedleft D) skewedright

Page18

2) Dataset:CaliforniaPickThreeLottery

8676091784

1575975399

8839889027

A) skewedleft B) symmetric C) uniform D) skewedright

3) Dataset:agesof20carsrandomlyselectedinastudentparkinglot

12 64911 17898

913 515 768821

A) symmetric B) uniform C) skewedleft D) skewedright

4) Dataset:systolicbloodpressuresof20randomlyselectedpatientsatabloodbank

135 120 115 132 136 124 119 145 98 110

125 120 115 130 140 105 116 121 125 108

A) symmetric B) uniform C) skewedleft D) skewedright

Provideanappropriateresponse.

5) Usethehistogrambelowtoapproximatethemodeheartrateofadultsinthegym.

A) 70 B) 42 C) 55 D) 2

Page19

6) Usethehistogrambelowtoapproximatethemedianheartrateofadultsinthegym.

A) 70 B) 65 C) 75 D) 42

7) Usethehistogrambelowtoapproximatethemeanheartrateofadultsinthegym.

A) 70.8 B) 1425.7 C) 70 D) 31.6

2 FindtheMean,Median,andMode

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Findthemean,median,andmodeofthefollowingnumbers:

73 76 69 73 66 74 73 67 68 71

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

2) Thetop14speeds,inmilesperhour,forPro–Stockdragracingoverthepasttwodecadesarelistedbelow.

Findthemeanspeed.

181.1 202.2 190.1 201.4 191.3 201.4 192.2

201.2 193.2 201.2 194.5 199.2 196.0 196.2

A) 195.8 B) 196.1 C) 201.2 D) 210.9

Page20

3) Thescoresofthetoptenfinishersinarecentgolftournamentarelistedbelow.Findthemeanscore.

71 67 67 72 76 72 73 68 72 72

A) 71 B) 67 C) 68 D) 72

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

4) ThenumbersofrunsbattedinthatSammySosahitinthefirst15yearsofhismajorleaguebaseballcareerare

listedbelow.Findthemeanandmediannumberofrunsbattedin.Roundthemeantothenearestwhole

number.

13 70 33 25 93 70 119 100

119 158 141 138 160 108 103

5) ThenumbersofhomerunsthatBarryBondshitinthefirst18yearsofhismajorleaguebaseballcareerare

listedbelow.Findthemeanandmediannumberofhomeruns.Roundthemeantothenearestwholenumber.

Whichmeasureofcentraltendency–themeanorthemedian–bestrepresentsthedata?Explainyour

reasoning.

16 25 24 19 33 25 34 46 37

33 42 40 37 34 49 73 46 45

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

6) Thetop14speeds,inmilesperhour,forPro–Stockdragracingoverthepasttwodecadesarelistedbelow.

Findthemedianspeed.

181.1 202.2 190.1 201.4 191.3 201.4 192.2

201.2 193.2 201.2 194.5 199.2 196.0 196.2

A) 196.1 B) 196.7 C) 195.8 D) 201.2

7) Thescoresofthetoptenfinishersinarecentgolftournamentarelistedbelow.Findthemedianscore.

67676871727272727376

A) 72 B) 67 C) 71 D) 73

8) Thetop14speeds,inmilesperhour,forPro–Stockdragracingoverthepasttwodecadesarelistedbelow.

Findthemodespeed.

181.1 202.2 190.1 201.4 191.3 201.4 192.2

201.2 193.2 201.2 194.5 199.2 196.0 196.2

imodal B) 201.4 C) 201.2 D) nomode

Page21

9) Thescoresofthetoptenfinishersinarecentgolftournamentarelistedbelow.Findthemodescore.

71 67 67 72 76 72 73 68 72 72

A) 72 B) 67 C) 76 D) 73

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

10) TheamountsofmoneywonbythetoptenfinishersinarecentDaytona500arelistedbelow.Findthemean

andmedianwinnings.Roundtothenearestdollar.Whichmeasure–themeanorthemedian–bestrepresents

thedata?Explainyourreasoning.

$2,194,246 $464,084 $164,096 $199,209 $438,834

$613,659 $142,884 $240,731 $145,809 $290,596

3 FindtheWeightedMean

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Astudentreceivestestscoresof62,83,and91.Thestudentʹsfinalexamscoreis88andhomeworkscoreis76.

Eachtestisworth20%ofthefinalgrade,thefinalexamis25%ofthefinalgrade,andthehomeworkgradeis

15%ofthefinalgrade.Whatisthestudentʹsmeanscoreintheclass?

A) 80.6 B) 76.6 C) 90.6 D) 85.6

2) Gradepointsareassignedasfollows:A=4,B=3,C=2,D=1,andF=O.Gradesareweightedaccordingto

credithours.IfastudentreceivesanAinafour–unitclass,aDinatwo–unitclass,aBinathree–unitclassand

aCinathree–unitclass,whatisthestudentʹsgradepointaverage?

A) 2.75 B) 1.75 C) 2.50 D) 3.00

4 FindtheMeanofGroupedData

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Approximatethemeanofthegroupeddata.

Miles(perday) Frequency

1–229

3–412

5–618

7–82

9–10 16

A) 5 B) 4 C) 6 D) 15

Phonecalls(perday) Frequency

8–11 17

12–15 29

16–19 16

20–23 46

24–27 34

A) 19 B) 18 C) 17 D) 20 E) 28

Page22

Weight(inpounds) Frequency

135–139 19

140–144 11

145–149 5

150–154 12

155–159 14

A) 146 B) 144 C) 148 D) 12

5 Concepts

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Whatisthedifferencebetweenusingμandxtorepresentamean?

2) Whydodataentriesneedtobeorderedbeforethemediancanbefound?

3) OnarecentStatisticstest,thescoreswere15,66,66,81,82,83,85,88,90,92,93,and95.Isthemeanagood

representationofthecenterofdata?Ifnot,why?

4) OnarecentStatisticstest,thescoreswere15,66,66,81,82,83,85,88,90,92,93,and95.Isthemodeagood

representationofthecenterofdata?Ifnot,why?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

5) OnarecentStatisticstest,thescoreswere61,66,68,82,84,86,88,90,92,and93.Findthe10%trimmedmean

ofthisdata.

A) 82 B) 77 C) 38.5 D) 85

6) Thelengthsofphonecallsfromonehousehold(inminutes)were2,4,6,7,and8 minutes.Findthemidrange

forthisdata.

A) 5minutes B) 2minutes C) 10minutes D) 6minutes

7) Thecostoffivehomesinacertainareaisgiven.

$147,000 $155,000 $175,000 $145,000 $1,225,000

Whichmeasureofcentraltendencyshouldbeused?

A) median B) mean C) mode D) midrange

8) Thecostoffivehomesinacertainareaisgiven.

$162,000 $170,000 $190,000 $160,000 $1,240,000

Listanyoutlier(s).

A) $1,240,000 B) $162,000

C) $1,240,000and$162,000 D) Therearenooutliers.

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9) Thecostoffivehomesinacertainareaisgiven.

$173,000 $181,000 $201,000 $171,000 $1,251,000

Calculatethemidrange.

A) $540,000 B) $181,000 C) $1,080,000 D) $395,400

2.4 MeasuresofVariation

1 FindMeasuresofVariation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Forthestem–and–leafplotbelow,findtherangeofthedataset.

Key:27=27

35

666789

77788999

01123445

6667889

01

A) 28 B) 41 C) 13 D) 34

2) Findtherangeofthedatasetrepresentedbythegraph.

A) 6 B) 17 C) 20 D) 5

3) Thegradepointaveragesfor10studentsarelistedbelow.Findtherangeofthedataset.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

A) 3.2 B) 2.45 C) 1.4 D) 2.8

Page24

4) Theheights(ininches)of20adultmalesarelistedbelow.Findtherangeofthedataset.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

A) 7 B) 5 C) 6 D) 6.5

5) Findthesamplestandarddeviation.

26159112214819

A) 7.1 B) 6.8 C) 2.1 D) 6.3

6) Findthesamplestandarddeviation.

1542537912142847

A) 17.8 B) 16.6 C) 29.1 D) 15.8

7) Findthesamplestandarddeviation.

2229212427282536

A) 4.8 B) 4.2 C) 1.6 D) 2.8

8) Theheights(ininches)of10adultmalesarelistedbelow.Findthesamplestandarddeviationofthedataset.

70 72 71 70 69 73 69 68 70 71

A) 1.49 B) 70 C) 3 D) 2.38

9) Sampleannualsalaries(inthousandsofdollars)forpublicelementaryschoolteachersarelisted.Findthe

samplestandarddeviation.

18.3 19.9 47.8 29.3 21.3 19.3

A) 11.40 B) 38.55 C) 4700.41 D) 4050.80

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

10) Theheights(ininches)ofall10adultmalesinanofficearelistedbelow.Findthepopulationstandard

deviationandthepopulationvariance.

70 72 71 70 69 73 69 68 70 71

11) Inarandomsample,10studentswereaskedtocomputethedistancetheytravelonewaytoschooltothe

nearesttenthofamile.Thedataislistedbelow.Computetherange,standarddeviationandvarianceofthe

data.

1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8

Page25

2 InterpretData

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Withoutperforminganycalculations,usethestem–and–leafplotstodeterminewhichstatementisaccurate.

(i)



9

58

3377

25

1

(ii)



9

58

3377

25

1

(iii)





5

33337777

5

A) Datasets(i)and(ii)havethesamestandarddeviation.

B) Dataset(ii)hasthegreateststandarddeviation.

C) Dataset(i)hasthesmalleststandarddeviation.

D) Datasets(i)and(iii)havethesamerange.

3 CompareTwoDataSets

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Youneedtopurchaseabatteryforyourcar.Therearetwotypesavailable.TypeAhasameanlifeoffiveyears

andastandarddeviationofoneyear.TypeBhasameanlifeoffiveyearsandastandarddeviationofone

month.Bothbatteriescostthesame.Whichoneshouldyoupurchaseifyouareconcernedthatyourcarwill

alwaysstart?Explainyourreasoning.

2) HerearethebattingaveragesofSammySosaandBarryBondsfor13recentyears.Whichplayerismore

consistent?Explainyourreasoning.

SammySosa 0.203 0.260 0.261

BarryBonds 0.292 0.311 0.336

0.300 0.268 0.273 0.251 0.308 0.288 0.320 0.328 0.288 0.279

0.312 0.294 0.308 0.291 0.303 0.262 0.306 0.328 0.370 0.341

3) Youarethemaintenanceengineerforalocalhighschool.Youmustpurchasefluorescentlightbulbsforthe

classrooms.ShouldyouchooseTypeAwithμ=3000hoursandσ=200hours,orTypeBwithμ=3000hours

andσ=250hours?

4 UsetheEmpiricalRule

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) ThemeanIQscoreofadultsis100,withastandarddeviationof15.UsetheEmpiricalRuletofindthe

percentageofadultswithscoresbetween70and130.(Assumethedatasethasabell –shapeddistribution.)

A) 95% B) 68% C) 99.7% D) 100%

2) Themeanscoreofaplacementexamforentranceintoamathclassis80,withastandarddeviationof10.Use

theEmpiricalRuletofindthepercentageofscoresthatliebetween60and80.(Assumethedatasethasa

bell–shapeddistribution.)

A) 47.5% B) 68% C) 34% D) 95%

Page26

3) ThemeanIQscoreofstudentsinaparticularcalculusclassis110,withastandarddeviationof5.Usethe

EmpiricalRuletofindthepercentageofstudentswithanIQabove120.(Assumethedatasethasabell –shaped

distribution.)

A) 2.5% B) 11.15% C) 13.5% D) 15.85%

4) Themeanscoreofacompetencytestis77

withastandarddeviationof4.UsetheEmpiricalRuletofindthe

percentageofscoresbetween69and85.(Assumethedatasethasabell–shapeddistribution.)

A) 95% B) 50% C) 99.7% D) 68%

5) Themeanscoreofacompetencytestis82,withastandarddeviationof2.Betweenwhattwovaluesdoabout

99.7%ofthevalueslie?(Assumethedatasethasabell–shapeddistribution.)

A) Between76and88 B) Between80and84 C) Between78and86 D) Between74and90

6) Themeanlengthofahumanpregnancyis265 days,withastandarddeviationof10days.UsetheEmpirical

Ruletodeterminethepercentageofwomenwhosepregnanciesarebetween255and275days.(Assumethe

datasethasabell–shapeddistribution.)

A) 68% B) 50% C) 95% D) 99.7%

7) ThemeanSATverbalscoreis428

withastandarddeviationof97.UsetheEmpiricalRuletodeterminewhat

percentofthescoresliebetween428and525.(Assumethedatasethasabell–shapeddistribution.)

A) 34% B) 68% C) 49.9% D) 47.5%

8) ThemeanSATverbalscoreis478

withastandarddeviationof98.UsetheEmpiricalRuletodeterminewhat

percentofthescoresliebetween380and478.(Assumethedatasethasabell–shapeddistribution.)

A) 34% B) 68% C) 49.9% D) 47.5%

9) ThemeanSATverbalscoreis412

withastandarddeviationof90.UsetheEmpiricalRuletodeterminewhat

percentofthescoresliebetween412and592.(Assumethedatasethasabell–shapeddistribution.)

A) 47.5% B) 68% C) 34% D) 49.9%

10) ThemeanSATverbalscoreis401

withastandarddeviationof97.UsetheEmpiricalRuletodeterminewhat

percentofthescoresliebetween207and498.(Assumethedatasethasabell–shapeddistribution.)

A) 81.5% B) 68% C) 34% D) 83.9%

11) Themeanmonthlyrentforasampleofstudioapartmentsinonecityis$1260 withastandarddeviationof

$230.Themonthlyrentsforeightmorestudioapartmentsinthecityarelisted.Usingthesamplestatistics

above,determinewhichofthedatavaluesareunusual.Areanyofthedatavaluesveryunusual?Explain.

(Assumethedatasethasabell–shapeddistribution.)

$1099,$1651,$1743,$1973,$846,$1789,$1398,$685

A) $1743

$1973

$1789

$685areunusualbecausetheyaremorethan2standarddeviationsfromthemean.

$1973isveryunusualbecauseitismorethan3standarddeviationsfromthemean.

B) $1651

$1743

$1973

$846

$1789

$685 areunusualbecausetheyaremorethan1standarddeviationfrom

themean.$1743,$1973,$1789,$685areveryunusualbecausetheyaremorethan2standarddeviations

fromthemean.

C) $1973isunusualbecauseitismorethan3standarddeviationsfromthemean.Therearenovaluesthat

areveryunusualbecausenovalueismorethan4standarddeviationsfromthemean.

D) $1743

$1973

$846

$1789

$685areunusualbecausetheyaremorethan2standarddeviationsfromthe

mean.$1973and$685areveryunusualbecausetheyaremorethan3standarddeviationsfromthemean.

Page27

5 UseChebychevʹsTheorem

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Heightsofadultwomenhaveameanof63.6in.andastandarddeviationof2.5in.DoesChebyshevʹsTheorem

sayaboutthepercentageofwomenwithheightsbetween58.6in.and68.6in.?

2) Heightsofadultwomenhaveameanof63.6in.andastandarddeviationof2.5in.ApplyChebyshevʹs

Theoremtothedatausingk=3.Interprettheresults.

6 UseGroupedDatatoCalculateaMeanandStandardDeviation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usethegroupeddataformulastofindtheindicatedmeanorstandarddeviation.

1) Thesalariesofarandomsampleofacompanyʹsemployeesaresummarizedinthefrequencydistribution

below.Approximatethesamplemean.

Salary($) Employees

5,001–10,000 14

10,001–15,000 16

15,001–20,000 14

20,001–25,000 17

25,001–30,000 19

A) $18,188.00 B) $17,500 C) $20,006.80 D) $16,369.20

2) Thespeedsofarandomsampleof100carsarerecordedastheypassahighwaycheckpoint.Theresultsare

summarizedinthefrequencydistributionbelow.Approximatethesamplemean.

Speed(mph) Cars

30–39 6

40–49 15

50–59 51

60–69 15

70–79 13

A) 55.9mph B) 54.5mph C) 61.5 mph D) 58.7 mph

3) Themanagerofabankrecordedtheamountoftimearandomsampleofcustomersspentwaitinginline

duringpeakbusinesshoursoneMonday.Thefrequencydistributionbelowsummarizestheresults.

Approximatethesamplemean.Roundyouranswertoonedecimalplace.

Waitingtime

(minutes)

Numberof

customers

0–312

4–715

8–11 12

12–15 4

16–19 7

20–23 2

24–27 2

A) 9.0min B) 13.5min C) 7.7 min D) 9.2 min

Page28

4) Theheightsofarandomsampleofprofessionalbasketballplayersaresummarizedinthefrequency

distributionbelow.Approximatethesamplemean.Roundyouranswertoonedecimalplace.

Height(in.) Frequency

70–71 3

72–73 4

74–75 15

76–77 14

78–79 12

80–81 5

82–83 2

A) 76.4in. B) 13.5in. C) 75.0 in. D) 77.8 in.

5) Arandomsampleof30highschoolstudentsisselected.Eachstudentisaskedhowmanyhoursheorshe

spentontheInternetduringthepreviousweek.Theresultsareshowninthehistogram.Estimatethesample

mean.

A) 7.9hr B) 7.7hr C) 8.1hr D) 8.3hr

6) Arandomsampleof25communityserviceprojectsisselectedandthescoresarerecorded.Theresultsare

showninthehistogram.Estimatethesamplemean.

A) 97.1 B) 97.3 C) 96.9 D) 96.7

Page29

7) Forthefollowingdataset,approximatethesamplestandarddeviation.

Miles(perday) Frequency

1–29

3–422

5–628

7–815

9–10 4

A) 2.1 B) 5.1 C) 2.9 D) 1.6

8) Forthefollowingdataset,approximatethesamplestandarddeviation.

Phonecalls(perday) Frequency

8–11 18

12–15 23

16–19 38

20–23 47

24–27 32

A) 5.1 B) 18.8 C) 2.9 D) 3.2

9) Forthefollowingdataset,approximatethesamplestandarddeviation.

Height(ininches) Frequency

50–52 5

53–55 8

56–58 12

59–61 13

62–64 11

A) 3.85 B) 1.86 C) 2.57 D) 0.98

10) Arandomsampleof30highschoolstudentsisselected.Eachstudentisaskedhowmanyhoursheorshe

spentontheInternetduringthepreviousweek.Theresultsareshowninthehistogram.Estimatethesample

standarddeviation.

A) 2.4hr B) 2.2hr C) 2.6hr D) 2.0hr

Page30

7 UseFormulastoAnalyzeData

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Inarandomsample,10studentswereaskedtocomputethedistancetheytravelonewaytoschooltothe

nearesttenthofamile.Thedataislistedbelow.Computethecoefficientofvariation.

1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8

2) Forthedatabelow,findPearsonʹsindexofskewness.Thedataset:Thesystolicbloodpressuresof20randomly

selectedpatientsatabloodbank.

130 120 115 132 136 124 119 145 98 110

125 120 115 130 140 105 116 121 125 108

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

3) Inarandomsample,10studentswereaskedtocomputethedistancetheytravelonewaytoschooltothe

nearesttenthofamile.Thedataislistedbelow.

a)Ifaconstantvaluekisaddedtoeachvalue,howwillthestandarddeviationbeaffected?

b)Ifeachvalueismultipliedbyaconstantk,howwillthestandarddeviationbeaffected?

1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8

A) Thestandarddeviationwillnotbeaffected.

B) Thestandarddeviationwillbemultipliedbytheconstantk.

2.5 MeasuresofPosition

1 CreateorInterpretaBox–and–whiskerPlot

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Thetestscoresof30studentsarelistedbelow.Findthefive–numbersummary.

31 41 45 48 52 55 56 58 63 65

67 67 69 70 70 74 75 78 79 79

80 81 83 85 85 87 90 92 95 99

A) Min=31,Q1=58,Q2=72,Q3=83,Max=99 B) Min=31,Q1=58,Q2=70,Q3=83,Max=99

C) Min=31,Q1=57,Q2=70,Q3=81,Max=99 D) Min=31,Q1=57,Q2=72,Q3=81,Max=99

2) Theweights(inpounds)of30preschoolchildrenarelistedbelow.Findthefive–numbersummary.

25 25 26 26.5 27 27 27.5 28 28 28.5

29 29 30 30 30.5 31 31 32 32.5 32.5

33 33 34 34.5 35 35 37 37 38 38

A) Min=25,Q1=28,Q2=30.75,Q3=34,Max=38

B) Min=25,Q1=28,Q2=30.5,Q3=34,Max=38

C) Min=25,Q1=27.5,Q2=30.75,Q3=33,Max=38

D) Min=25,Q1=27.5,Q2=30.5,Q3=33.5,Max=38

Page31

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

3) Theweights(inpounds)of30preschoolchildrenarelistedbelow.Findtheinterquartilerangeofthe30

weightslistedbelow.Whatcanyouconcludefromtheresult?

25 25 26 26.5 27 27 27.5 28 28 28.5

29 29 30 30 30.5 31 31 32 32.5 32.5

33 33 34 34.5 35 35 37 37 38 38

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

4) Thecholesterollevels(inmilligramsperdeciliter)of30adultsarelistedbelow.Findtheinterquartilerangefor

thecholesterollevelofthe30adults.

154 156 165 165 170 171 172 180 184 185

189 189 190 192 195 198 198 200 200 200

205 205 211 215 220 220 225 238 255 265

A) 31 B) 30 C) 211 D) 180

5) Thecholesterollevels(inmilligramsperdeciliter)of30adultsarelistedbelow.FindQ1.

154156165165170171172180184185

189189190192195198198200200200

205205211215220220225238255265

A) 180 B) 200 C) 184.5 D) 171

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

6) Thetestscoresof30studentsarelistedbelow.Drawabox–and–whiskerplotthatrepresentsthedata.

31 41 45 48 52 55 56 56 63 65

67 67 69 70 70 74 75 78 79 79

80 81 83 85 85 87 90 92 95 99

7) Thecholesterollevels(inmilligramsperdeciliter)of30adultsarelistedbelow.Drawabox–and–whiskerplot

thatrepresentsthedata.

154 156 165 165 170 171 172 180 184 185

189 189 190 192 195 198 198 200 200 200

205 205 211 215 220 220 225 238 255 265

Page32

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

8) Usethebox–and–whiskerplotbelowtodeterminewhichstatementisaccurate.

A) Onehalfofthecholesterollevelsarebetween180and211.

B) Onehalfofthecholesterollevelsarebetween180and197.5.

C) About25%oftheadultshavecholesterollevelsofatmost211.

D) About75%oftheadultshavecholesterollevelslessthan180.

2 CalculateorComparez–scores

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Findthez–scoreforthevalue55

whenthemeanis58 andthestandarddeviationis3.

A) z=–1.00 B) z=–1.33 C) z= –0.90 D) z=0.90

2) Manyfirmsuseon–the–

obtrainingtoteachtheiremployeescomputerprogramming.Supposeyouworkin

thepersonneldepartmentofafirmthatjustfinishedtrainingagroupofitsemployeestoprogram,andyou

havebeenrequestedtoreviewtheperformanceofoneofthetraineesonthefinaltestthatwasgiventoall

trainees.Themeanandstandarddeviationofthetestscoresare72and5,respectively,andthedistributionof

scoresisbell–shapedandsymmetric.Supposethetraineeinquestionreceivedascoreof68.Computethe

traineeʹsz–score.

A) z=–0.80 B) z=0.8 C) z= –0.88 D) z=0.88

3) Aradiostationclaimsthattheamountofadvertisingperhourofbroadcasttimehasanaverageof17 minutes

andastandarddeviationequalto2.2minutes.Youlistentotheradiostationfor1hour,atarandomlyselected

time,andcarefullyobservethattheamountofadvertisingtimeisequalto15minutes.Calculatethez–scorefor

thisamountofadvertisingtime.

A) z=–0.91 B) z=0.91 C) z= –0.75 D) z=0.75

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

4) Testscoresforahistoryclasshadameanof79withastandarddeviationof4.5.Testscoresforaphysicsclass

hadameanof69withastandarddeviationof3.7.Supposeastudentgetsa83onthehistorytestanda84on

thephysicstest.Calculatethez–scoreforeachtest.Onwhichtestdidthestudentperformbetter?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

5) ForthemathematicspartoftheSATthemeanis514withastandarddeviationof113,andforthemathematics

partoftheACTthemeanis20.6withastandarddeviationof5.1.Bobscoresa660ontheSATanda27onthe

ACT.Usez–scorestodetermineonwhichtestheperformedbetter.

A) SAT B) ACT

Page33

6) Thebirthweightsfortwinsarenormallydistributedwithameanof2353gramsandastandarddeviationof

647grams.Usez–scorestodeterminewhichbirthweightcouldbeconsideredunusual.

A) 3647g B) 1200g C) 2000g D) 2353g

3 FindtheMidquartile

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Theagesof10groomsattheirfirstmarriagearelistedbelow.Findthemidquartile.

35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9

A) 34.2 B) 43.7 C) 34.1 D) 34.5

4 FindaPercentile

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Thecholesterollevels(inmilligramsperdeciliter)of30adultsarelistedbelow.FindD6.

154 156 165 165 170 171 172 180 184 185

189 189 190 192 195 198 198 200 200 200

205 205 211 215 220 220 225 238 255 265

A) 200 B) 265 C) 171 D) 205

2) Thetestscoresof30studentsarelistedbelow.FindP30.

31 41 45 48 52 55 56 56 63 65

67 67 69 70 70 74 75 78 79 79

80 81 83 85 85 87 90 92 95 99

A) 63 B) 56 C) 67 D) 90

3) Thetestscoresof30studentsarelistedbelow.FindP81.

31 41 45 48 52 55 56 56 63 65

67 67 69 70 70 74 75 78 79 79

80 81 83 85 85 87 90 92 95 99

A) 86 B) 56 C) 67 D) 90

4) Theweights(inpounds)of30preschoolchildrenarelistedbelow.FindD7.

25252626.5272727.5282828.5

2929303030.531313232.532.5

33333434.5353537373838

A) 33 B) 31 C) 37 D) 27

5) Ateachergivesa20–pointquizto10students.Thescoresarelistedbelow.Whatpercentilecorrespondstothe

scoreof12?

20 810 715 16 12 19 14 9

A) 40 B) 13 C) 25 D) 12

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6) Inadatasetwithaminimumvalueof54.5andamaximumvalueof98.6with300observations,thereare186

pointslessthan81.2.Findthepercentilefor81.2.

A) 62 B) 71 C) 68 D) 53

7) Thecholesterollevels(inmilligramsperdeciliter)of30adultsarelistedbelow.Findthepercentilethat

correspondstocholesterollevelof195.

154 156 165 165 170 171 172 180 184 185

189 189 190 192 195 198 198 200 200 200

205 205 211 215 220 220 225 238 255 265

A) 50 B) 12 C) 33 D) 58

5 Concepts

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) AstudentʹsscoreontheSAT–1placementtestforU.S.historyisinthe90thpercentile.Whatcanyouconclude

aboutthestudentʹstestscore?

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Ch.2 DescriptiveStatistics

AnswerKey

2.1 FrequencyDistributionsandTheirGraphs

1 InterpretaFrequencyDistribution

2 InterpretFrequencyDistributionGraphs

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3 ConstructaFrequencyDistributionfromDataSet

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2.2 MoreGraphsandDisplays

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2 GraphDataSets

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2.3 MeasuresofCentralTendency

1 InterprettheGraphofaDistribution

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2 FindtheMean,Median,andMode

3 FindtheWeightedMean

4 FindtheMeanofGroupedData

5 Concepts

2.4 MeasuresofVariation

1 FindMeasuresofVariation

2 InterpretData

3 CompareTwoDataSets

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4 UsetheEmpiricalRule

5 UseChebychevʹsTheorem

6 UseGroupedDatatoCalculateaMeanandStandardDeviation

7 UseFormulastoAnalyzeData

2.5 MeasuresofPosition

1 CreateorInterpretaBox–and–whiskerPlot

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2 CalculateorComparez–scores

3 FindtheMidquartile

4 FindaPercentile

5 Concepts

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