Chapter 02 Sample Annual Salaries In Thousands Dollars

Unlock access to all the studying documents.

View Full Document

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10

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

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

Usethemaximumandminimumdataentriesandthenumberofclassestofindtheclasswidth,thelowerclasslimits,

andtheupperclasslimits.

5) min=1,max=30,6classes

6) min=80,max=265,6classes

2 InterpretFrequencyDistributionGraphs

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

Provideanappropriateresponse.

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

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

Page11

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

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

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

Usetherelativefrequencyhistogramto

a)identifytheclasswiththegreatest,andtheclasswiththeleast,relativefrequency.

b)approximatethegreatestandleastrelativefrequencies.

c)approximatetherelativefrequencyofthefifthclass.

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

polygon.

4) Height(ininches)

Class Frequency,f

50–52 5

53–55 8

56–58 12

59–61 13

62–64 11

Page12

5) 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.

6) PhoneCalls(perday)

Class Frequency,f

8–11 18

12–15 23

16–19 38

20–23 47

24–27 32

7) Height(ininches)

Class Frequency,f

50–52 5

53–55 8

56–58 12

59–61 13

62–64 11

8) Weight(inpounds)

Class Frequency,f

135–139 6

140–144 4

145–149 11

150–154 15

155–159 8

9) Miles(perday)

Class Frequency,f

1–29

3–422

5–628

7–815

9–10 4

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91 degreesFahrenheitanditslowest

temperatureat12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) 12–19 B) 12–20 C) 7–17 D) 12–18

Page13

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.

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.

Page14

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?

4Concepts

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

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

Matchthedescriptionofthesamplewiththecorrectplot.

1) Time(inminutes)ittakesasampleofemployeestodrivetowork

A) B)

C) Key:09=0.9

0

1

2

3

4

9

49

3678

01568

0

D) Key:72=72

6

7

8

9

89

0233678

2456778

0115

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

Provideanappropriateresponse.

2) 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

3) 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15

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

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

Key:11 9=11.9

69

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

78

A) max:17.8;min:11.6 B) max:178;min:116

C) max:17.7;min:11.6 D) max:17.8;min:11.9

5) 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.

6) 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

7) 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16

2 GraphDataSets

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

Provideanappropriateresponse.

1) Displaythedatabelowinastem–and–leafplot.

8

0455677799

0224589

1

8

9

456688899

0114589

1

8

0466788899

0224579

1

8

0

7

1

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

2) 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

3) 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

Page17

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 69

Onlineservices 124

Executivesearchfirms 72

Mailings 32

Networking 103

Constructapiechartofthedata.

5) 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.

6) 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

7) 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

8) 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

Page18

9) 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

10) 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

11) 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

12) 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

Page19

13) 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

14) 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

15) 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

16) 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

17) 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

18) 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

Page20

19) 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

20) 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

21) Thegraphbelowshowsthenumberofcaraccidentsoccurringinonecityineachoftheyears1through6.The

numberofaccidentsdroppedinyear3afteranewspeedlimitwasimposed.Doesthegraphdistortthedata?

Howwouldyouredesignthegraphtobelessmisleading?

Page21

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.

Provideanappropriateresponse.

1) Determinewhethertheapproximateshapeofthedistributioninthehistogramissymmetric,uniform,skewed

left,skewedright,ornoneofthese.

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

2) Determinewhethertheapproximateshapeofthedistributioninthehistogramissymmetric,uniform,skewed

left,skewedright,ornoneofthese.

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

Page22

3) Findthemean,median,andmodeofthedata.

A) x=70;median=69;mode=67 B) x≈70.1;median=69;mode=68

C) x≈70.3;median=69;mode=68 D) x=70;median=67;mode=69

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.

4) 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

5) 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

6) 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

7) 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

Page23

Provideanappropriateresponse.

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

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

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

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

10) 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

Page24

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:

65 68 61 65 58 66 65 59 60 63

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

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

Page25

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:201.2,201.4 B) 201.4

C) 201.2 D) nomode

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

3Find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=0.Gradesareweightedaccordingto

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

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

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

Page26

4 FindtheMeanofFrequencyDistribution

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

Approximatethemeanofthefrequencydistribution.

Miles(perday) Frequency

1–215

3–428

5–611

7–814

9–10 9

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

Phonecalls(perday) Frequency

8–11 37

12–15 49

16–19 17

20–23 46

24–27 39

A) 18 B) 17 C) 16 D) 19 E) 38

Weight(inpounds) Frequency

135–139 7

140–144 12

145–149 10

150–154 11

155–159 20

A) 149 B) 147 C) 151 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97.Findthe10%trimmedmean

ofthisdata.

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

Page27

6) Thelengthsofphonecallsfromonehousehold(inminutes)were2,4,6,7,and10minutes.Findthemidrange

forthisdata.

A) 6minutes B) 2minutes C) 10minutes D) 7minutes

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

$141,000 $149,000 $169,000 $139,000 $1,219,000

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.

$186,000 $194,000 $214,000 $184,000 $1,264,000

Listanyoutlier(s).

A) $1,264,000 B) $186,000

C) $1,264,000and$186,000 D) Therearenooutliers.

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

$206,000 $214,000 $234,000 $204,000 $1,284,000

Calculatethemidrange.

A) $540,000 B) $214,000 C) $1,080,000 D) $428,400

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

4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3

A) 29 B) 43 C) 14 D) 37

Page28

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

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

Page29

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

samplestandarddeviation.

17.0 10.7 38.7 32.1 16.4 15.9

A) 10.97 B) 35.40 C) 3453.36 D) 2851.44

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

2Interpret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.

Page30

2) Youareaskedtocomparethreedatasets.Withoutcalculating,determinewhichdatasethasthegreatest

samplestandarddeviationandwhichhastheleastsamplestandarddeviation.

(i)

(ii)

(iii)

A) Greatestsamplestandarddeviation:(i)

Leastsamplestandarddeviation:(iii)

B) Greatestsamplestandarddeviation:(i)

Leastsamplestandarddeviation:(ii)

C) Greatestsamplestandarddeviation:(iii)

Leastsamplestandarddeviation:(ii)

D) Greatestsamplestandarddeviation:(iii)

Leastsamplestandarddeviation:(i)

3) Youareaskedtocomparethreedatasets.Withoutcalculating,determinewhichdatasethasthegreatest

samplestandarddeviationandwhichhastheleastsamplestandarddeviation.

(i) (ii) (iii)

2

3

4

5

6

4

003399

8

1

2

3

4

5

6



4

00033399

8

2

3

4

5

6

45

0399

89

1

A) Greatestsamplestandarddeviation:(iii)

Leastsamplestandarddeviation:(ii)

B) Greatestsamplestandarddeviation:(iii)

Leastsamplestandarddeviation:(i)

C) Greatestsamplestandarddeviation:(i)

Leastsamplestandarddeviation:(ii)

D) Greatestsamplestandarddeviation:(i)

Leastsamplestandarddeviation:(iii)

Page31

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%

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65

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

percentageofscoresbetween53and77.(Assumethedatasethasabell–shapeddistribution.)

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

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266 days,withastandarddeviationof9days.UsetheEmpirical

Ruletodeterminethepercentageofwomenwhosepregnanciesarebetween257and275days.(Assumethe

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

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

Page32

7) ThemeanSATverbalscoreis462

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

percentofthescoresliebetween462and560.(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486

withastandarddeviationof95.UsetheEmpiricalRuletodeterminewhat

percentofthescoresliebetween391and486.(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500

withastandarddeviationof100.UsetheEmpiricalRuletodeterminewhat

percentofthescoresliebetween500and700.(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490

withastandarddeviationof96.UsetheEmpiricalRuletodeterminewhat

percentofthescoresliebetween298and586.(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$1200 withastandarddeviationof

$210.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.)

$1074,$1536,$1641,$528,$801,$1662,$1347,$696

A) $1641

$528

$1662

$696areunusualbecausetheyaremorethan2standarddeviationsfromthemean.

$528isveryunusualbecauseitismorethan3standarddeviationsfromthemean.

B) $1536

$1641

$528

$801

$1662

$696 areunusualbecausetheyaremorethan1standarddeviationfrom

themean.$1641,$528,$1662,$696areveryunusualbecausetheyaremorethan2standarddeviations

fromthemean.

C) $528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) $1641

$528

$801

$1662

$696areunusualbecausetheyaremorethan2standarddeviationsfromthe

mean.$528and$696areveryunusualbecausetheyaremorethan3standarddeviationsfromthemean.

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.

Page33

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 16

10,001–15,000 14

15,001–20,000 11

20,001–25,000 16

25,001–30,000 23

A) $18,500.50 B) $17,500 C) $20,350.55 D) $16,650.45

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 3

40–49 17

50–59 50

60–69 19

70–79 11

A) 56.3mph B) 54.5mph C) 61.9 mph D) 59.1 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–714

8–11 13

12–15 6

16–19 8

20–23 2

24–27 1

A) 9.1min B) 13.5min C) 8.0 min D) 9.2 min

Page34

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 1

72–73 6

74–75 8

76–77 12

78–79 9

80–81 5

82–83 2

A) 76.6in. B) 13.5in. C) 74.9 in. D) 78.4 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35

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36

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) 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.

2) 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.

8 ComputetheCoefficientofVariation

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

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

Findthecoefficientofvariationforeachofthetwosetsofdata,thencomparethevariation.Roundresultstoone

decimalplace.

2) Listedbelowarethesystolicbloodpressures(inmmHg)forasampleofmenaged20–29andforasampleof

menaged60–69.

Menaged20–29: 118 124 129 118 131 123

Menaged60–69: 131 151 137 125 164 139

A) Menaged20–29:4.4%

Menaged60–69:10.0%

Thereissubstantiallymorevariationinbloodpressuresofthemenaged60–69.

B) Menaged20–29:4.6%

Menaged60–69:10.5%

Thereissubstantiallymorevariationinbloodpressuresofthemenaged60–69.

C) Menaged20–29:4.2%

Menaged60–69:8.1%

Thereissubstantiallymorevariationinbloodpressuresofthemenaged60 –69.

D) Menaged20–29:7.2%

Menaged60–69:4.6%

Thereismorevariationinbloodpressuresofthemenaged20–29.

Page37

3) Thecustomerservicedepartmentofaphonecompanyisexperimentingwithtwodifferentsystems.On

Mondaytheytrythefirstsystemwhichisbasedonanautomatedmenusystem.OnTuesdaytheytrythe

secondsysteminwhicheachcallerisimmediatelyconnectedwithaliveagent.Aqualitycontrolmanager

selectsasampleofsevencallseachday.Herecordsthetimeforeachcustomertohavehisorherquestion

answered.Thetimes(inminutes)arelistedbelow.

AutomatedMenu: 11.2 7.2 4.0 2.9 9.2 6.3 5.5

Liveagent: 6.3 2.5 4.8 4.1 3.4 5.2 3.7

A) AutomatedMenu:43.7%

Liveagent:29.4%

Thereissubstantiallymorevariationinthetimesfortheautomatedmenusystem.

B) AutomatedMenu:45.3%

Liveagent:30.5%

Thereissubstantiallymorevariationinthetimesfortheautomatedmenusystem.

C) AutomatedMenu:46.9%

Liveagent:31.5%

Thereissubstantiallymorevariationinthetimesfortheautomatedmenusystem.

D) AutomatedMenu:24.3%

Liveagent:46.2%

Thereissubstantiallymorevariationinthetimesfortheliveagent.

4) Comparethevariationinheightstothevariationinweightsofthirteen–yearoldgirls.Theheights(ininches)

andweights(inpounds)ofninerandomlyselectedthirteen–yearoldgirlsarelistedbelow.

Heights(inches): 59.3 61.2 62.6 64.7 60.1 58.3 64.6 63.7 66.1

Weights(pounds): 86 97 93 119 96 90 123 98 139

A) Heights:4.3%

Weights:17.2%

Thereissubstantiallymorevariationintheweightsthanintheheightsofthegirls.

B) Heights:4.1%

Weights:16.4%

Thereissubstantiallymorevariationintheweightsthanintheheightsofthegirls.

C) Heights:3.9%

Weights:15.4%

Thereissubstantiallymorevariationintheweightsthanintheheightsofthegirls.

D) Heights:11.5%

Weights:6.5%

Thereissubstantiallymorevariationintheheightsthanintheweightsofthegirls.

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

Page38

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

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

6) Usethedatatoidentifyanyoutliers.

35 40 54 65 67

69 71 73 74 76

80 82 87 90 99

A) 35

40 B) 35

99 C) 35 D) None

7) Usethedatatoidentifyanyoutliers.

16 25 133 15

518 820 14

17 19 16 10 21

28 14 37 18

A) 1,33

37 B) 1,37 C) 33

37 D) None

Page39

8) Usethedatatoidentifyanyoutliers.

15 18 18 19 22 23 24

24 24 24 25 26 26 27

28 28 30 32 33 40 42

A) 40,42 B) 42 C) 15,42 D) None

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

9) 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

10) 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

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

11) 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.

Page40

2 CalculateorComparez–scores

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

Provideanappropriateresponse.

1) ThemidpointsA,B,andCaremarkedonthehistogram.Withoutcalculating,matchthemwiththeindicated

z–scores.Whichz–scores,ifany,wouldbeconsideredunusual?

z=0

z=-1.33

z=2.01

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

2) Findthez–scoreforthevalue62

whenthemeanis79 andthestandarddeviationis4.

A) z=-4.25 B) z=-4.50 C) z=-0.73 D) z=0.73

3) 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81and3,respectively,andthedistributionof

scoresisbell–shapedandsymmetric.Supposethetraineeinquestionreceivedascoreof77.Computethe

traineeʹsz–score.

A) z=-1.33 B) z=1.33 C) z=-0.91 D) z=0.91

4) 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2.7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11minutes.Calculatethez–scorefor

thisamountofadvertisingtime.

A) z=-2.22 B) z=2.22 C) z=-0.49 D) z=0.49

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

5) 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65onthehistorytestanda74on

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

Page41

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

6) 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

7) 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graphbelowisanogiveofscoresonamathtest.

PercentileRanksofMathTestScores

10 20 30 40 50 60 70 80 90 100

100

Test Score

Percentile

10 20 30 40 50 60 70 80 90 100

100

Test Score

Percentile

Usethegraphtoapproximatethepercentilerankofanindividualwhosetestscoreis70.

A) 53 B) 80 C) 58 D) 75

Page42

2) Thegraphbelowisanogiveofscoresonamathtest.

PercentileRanksofMathTestScores

10 20 30 40 50 60 70 80 90 100

100

Test Score

Percentile

10 20 30 40 50 60 70 80 90 100

100

Test Score

Percentile

Usethegraphtoapproximatethetestscorethatcorrespondstothe10thpercentile?

A) 40 B) 1 C) 34 D) 6

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

correspondstoacholesterollevelof238milligramsperdeciliter.

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) 90thpercentile B) 30thpercentile C) 40thpercentile D) 50thpercentile

4) Thetestscoresof30studentsarelistedbelow.Findthepercentilethatcorrespondstoascoreof74.

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) 50thpercentile B) 90thpercentile C) 30thpercentile D) 40thpercentile

5) Thetestscoresof30studentsarelistedbelow.Whichtestscoresareabovethe75thpercentile?

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) 85,85,87,90,92,95,99 B) 90,92,95,99

C) 83,85,85,87,90,92,95,99 D) 87,90,92,95,99

Page43

6) Theweights(inpounds)of30preschoolchildrenarelistedbelow.Whichweightsarebelowthe25th

percentile?

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) 25,25,26,26.5,27,27,27.5 B) 25,25,26,26.5,27,27,27.5,28,28

C) 25,25,26,26.5,27,27 D) 25,25,26,26.5

7) 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

8) 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

9) 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?

Page44

Ch.2 DescriptiveStatistics

AnswerKey

2.1 FrequencyDistributionsandTheirGraphs

1 InterpretaFrequencyDistribution

2 InterpretFrequencyDistributionGraphs

Page45

Page46

Page47

Page48

Page49

Page50

Page51

Page52

4 Concepts

2.2 MoreGraphsandDisplays

1 InterpretDataSets

Page53

2 GraphDataSets

Page54

Page55

Page56

Page58

Page59

2.3 MeasuresofCentralTendency

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

2 FindtheMean,Median,andMode

3FindtheWeightedMean

4 FindtheMeanofFrequencyDistribution

5 Concepts

2.4 MeasuresofVariation

1 FindMeasuresofVariation

2 InterpretData

Page61

3 CompareTwoDataSets

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

8 ComputetheCoefficientofVariation

2.5 MeasuresofPosition

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

Page62

2 CalculateorComparez–scores

3 FindtheMidquartile

4 FindaPercentile

5 Concepts

Page63