CH2 - solution of chapter 2 PDF

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Summary

Chapter 2 Descriptive Statistics: Tabular and Graphical Displays Learning Objectives 1. Learn how to construct and interpret summarization procedures for qualitative data such as: frequency and relative frequency distributions, bar graphs and pie charts. 2. Learn how to construct and interpret tabul...

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Cha pt e r2 De s c r i pt i v eSt a t i s t i c s :Ta bul a ra nd Gr a phi c a lDi s pl a y s Le a r ni ngObj e c t i v e s 1.

Le a r nho wt oc o ns t r u c ta n di nt e r pr e ts umma r i z a t i onpr oc e dur e sf orq ua l i t a t i v eda t as u c ha s : f r e que nc ya ndr e l a t i vef r e que nc ydi s t r i but i ons , b a rgr a phsa n dp i ec h a r t s .

2.

Le a r nho wt oc o ns t r uc ta ndi nt e r pr e tt a b ul a rs umma r i z a t i onpr o c e dur e sf o rqua nt i t a t i v ed a t as uc ha s : f r e que nc ya ndr e l a t i vef r e que nc ydi s t r i but i ons ,c umul a t i v ef r e que nc ya ndc umul a t i ver e l a t i ve f r e que nc ydi s t r i but i ons .

3.

Le a r nho wt oc o ns t r uc tadotpl o ta ndahi s t ogr a ma sgr a ph i c a ls umma r i e sofqua nt i t a t i v eda t a .

4.

Le a r nho wt hes ha peofada t ad i s t r i but i oni sr e v e a l e db yahi s t o gr a m. Le a r nho wt or e c o gni z ewh e na da t ad i s t r i but i oni sne ga t i v e l ys ke we d, s ymme t r i c ,a ndpos i t i v e l ys ke we d .

5.

Bea bl et ous ea ndi nt e r pr e tt hee xpl or a t or yda t aa na l y s i st e c hni queofas t e ma ndl e a fdi s pl a y .

6.

Le a r nho wt oc o ns t r uc ta ndi nt e r pr e tc r o s st a b ul a t i ons ,s c a t t e rdi a gr a ms ,s i de b y s i dea nds t a c ke dba r c ha r t s .

7.

Le a r nbe s tpr a c t i c e sf orc r e a t i n ge ffe c t i v egr a phi c a ldi s pl a y sa ndf orc ho os i n gt hea ppr opr i a t et y peo f di s pl a y .

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Cha pt e r2

Sol ut i ons : 1. Class A B C

Frequency 60 24 36 120

Relative Frequency 60/120 = 0.50 24/120 = 0.20 36/120 = 0.30 1.00

2. a . 1–( . 22+. 18+. 40)=. 20 b .. 20( 20 0)=40 c / d. Cl a s s A B C D Tot a l

Fr e q ue n c y Pe r c e ntFr e q ue nc y . 22( 20 0)=44 22 . 18( 20 0)=36 18 . 40( 20 0)=80 40 . 20( 20 0)=40 20 200 10 0

3. a . 360°x58/ 120=174° b . 360°x42/ 120=126° c .

Object3

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De s c r i pt i v eSt a t i s t i c s :Ta bul a ra ndGr a p hi c a lDi s pl a ys

d .

Object5

4.

a.

These data are categorical.

b. Show Jep

Relative Frequency

% Frequency

10

20

JJ

8

16

OWS

7

14

THM

12

24

WoF

13

26

Total

50

100

c.

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Cha pt e r2

Object7

Object9

d.

5.

The largest viewing audience is for Wheel of Fortune and the second largest is for Two and a Half Men.

a. Relative

Percent

Frequency

Frequency

Frequency

Brown

7

0.14

14%

Johnson

Name

b.

c. d. The three Smith (24%), Johnson

10

0.20

20%

Jones

7

0.14

14%

Miller

6

0.12

12%

Smith

12

0.24

24%

8

0.16

16%

1

100%

Williams 6.

a.

Total:

50 Relative

most common last names are (20%), Williams (16%5)

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De s c r i pt i v eSt a t i s t i c s :Ta bul a ra ndGr a p hi c a lDi s pl a ys

Network

Frequency

% Frequency

ABC

6

24

CBS

9

36

FOX

1

4

NBC

9

36

Total:

25

100

Object17

b.

For these data, NBC and CBS tie for the number of top-rated shows. Each has 9 (36%) of the top 25. ABC is third with 6 (24%) and the much younger FOX network has 1(4%).

7. a . Rating Excellent Very Good Good Fair Poor

Frequency 20 23 4 1 2 50

Percent Frequency 40 46 8 2 4 100

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Cha pt e r2

Object19

Ma na g e me nts houl dbev e r ypl e a s e dwi t ht hes ur v e yr e s ul t s .40% +46% =86% oft her a t i ng sa r e v e r yg oodt oe x c e l l e nt .94% oft her a t i n g sa r eg oodorbe t t e r .Thi sdoe sno tl ookt obeaDe l t afli ght whe r es i gn i fic a ntc ha n g e sa r en e e de dt oi mp r o v et heo v e r a l lc us t ome rs a t i s f a c t i onr a t i n gs . b . Whi l et heo v e r a l lr a t i n gsl ookfine ,not et ha tonec us t ome r( 2%)r a t e dt heo v e r a l le xpe r i e nc ewi t ht he fli ghta sFa i ra ndt woc us t ome r s( 4%)r a t e dt heo v e r a l le xpe r i e nc ewi t ht hefli gh ta sPo or .I tmi ghtbe i ns i ght f ulf ort hema na g e rt or e vi e we xpl a na t i onsf r omt h e s ec us t ome r sa st oh o wt hefli ghtf a i l e dt o me e te xpe c t a t i ons .Pe r ha ps , i twa sa ne xpe r i e nc ewi t ho t he rpa s s e n g e r st ha tDe l t ac o ul ddol i t t l et o c or r e c torpe r ha psi twa sa ni s ol a t e di nc i de n tt ha tDe l t ac o ul dt a k es t e pst oc or r e c ti nt hef ut ur e . 8. a . Position Pitcher Catcher 1st Base 2nd Base 3rd Base Shortstop Left Field Center Field Right Field

Frequency 17 4 5 4 2 5 6 5 7 55

Relative Frequency 0.309 0.073 0.091 0.073 0.036 0.091 0.109 0.091 0.127 1.000

b . Pi t c he r s( Al mos t31%) c . 3r dBa s e( 3–4%) d . Ri gh tFi e l d( Al mos t13%) e .I nfie l de r s( 16or29. 1%)t oOut fie l de r s( 18or32. 7%) 9.

a.

Living Area City Suburb Small Town Rural Area Total

Live Now 32% 26% 26% 16% 100%

Ideal Community 24% 25% 30% 21% 100% 2-6

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De s c r i pt i v eSt a t i s t i c s :Ta bul a ra ndGr a p hi c a lDi s pl a y s

b.

Where do you live now?

Object21

What do you consider the ideal community?

Object24

c.

Most adults are now living in a city (32%).

d.

Most adults consider the ideal community a small town (30%).

e.

Percent changes by living area: City –8%, Suburb –1%, Small Town +4%, and Rural Area +5%. Suburb living is steady, but the trend would be that living in the city would decline while living in small towns and rural areas would increase.

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Cha pt e r2

Rating Excellent

Frequency 20

Good

101

Fair

528

Bad

244

Terrible

122

Total

1015

Rating

Percent Frequency

b.

Excellent

2

Good

10

Fair

52

Bad

24

Terrible

12

Total

100

c.

Object27

d.

24% + 12% = 36% of adults in the United Sates think the Federal Bank is doing a bad or a terrible job in handling the credit problems. Only 10% + 2% = 12% think the Federal Bank is doing a good or excellent job.

e.

40% + 10% = 50% of adults in Spain think the European Central Bank is doing a bad or terrible job in handling the credit problems. Only 4% of adults in Spain think the European Central Bank is doing a good or excellent job. Both countries show pessimism and relatively low confidence in how the banks are handling the credit problems in the financial markets. But in comparing the two countries, adults in Spain show more concern and more pessimism about the bank’s ability compared to adults in the United States.

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De s c r i pt i v eSt a t i s t i c s :Ta bul a ra ndGr a p hi c a lDi s pl a y s

Cl a s s Fr e q ue n c y 12–1 4 2 15–1 7 8 18–2 0 11 21–2 3 10 24–2 6 9 Tot a l 40

Re l a t i v eFr e q ue nc y 0. 050 0. 200 0. 275 0. 250 0. 225 1. 000

Pe r c e ntFr e que nc y 5 . 0 20. 0 27. 5 25. 0 22. 5 100 . 0

12. Class less than or equal to 19 less than or equal to 29 less than or equal to 39 less than or equal to 49 less than or equal to 59

Cumulative Frequency 10 24 41 48 50

Cumulative Relative Frequency .20 .48 .82 .96 1.00

13.

Object30

14.a .













b/ c . Class 6.0 – 7.9 8.0 – 9.9 10.0 – 11.9 12.0 – 13.9 14.0 – 15.9 15.

Frequency 4 2 8 3 3 20

Percent Frequency 20 10 40 15 15 100

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Cha pt e r2

6

3

7

557

8

1348

9

36

10 0 4 5 11 3 16.

Le a fUni t=10 11 6 12 0 2 13 0 6 7 14 2 2 7 15 5 16 0 2 8 17 0 2 3

17.a / b. Waiting Time 0–4 5–9 10 – 14 15 – 19 20 – 24 Totals

Frequency 4 8 5 2 1 20

Relative Frequency 0.20 0.40 0.25 0.10 0.05 1.00

c / d. Waiting Time Less than or equal to 4 Less than or equal to 9 Less than or equal to 14 Less than or equal to 19 Less than or equal to 24

Cumulative Frequency 4 12 17 19 20

Cumulative Relative Frequency 0.20 0.60 0.85 0.95 1.00

e . 12/ 20=0. 60 18.a. Salary 150–159 160–169 170–179 180–189 190–199 200–209 210–219 Total

Frequency 1 3 7 5 1 2 1 20 2-10

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De s c r i pt i v eSt a t i s t i c s :Ta bul a ra ndGr a p hi c a lDi s pl a y s

b. Salary 150–159 160–169 170–179 180–189 190–199 200–209 210–219 Total

Percent Frequency 5 15 35 25 5 10 5 100

c. Cumulative Percent Frequency

Salary Less than or equal to 159

5

Less than or equal to 169

20

Less than or equal to 179

55

Less than or equal to 189

80

Less than or equal to 199

85

Less than or equal to 209

95

Less than or equal to 219

100

Total

100

d.

Object33

e.

There is skewness to the right.

f.

(3/20)(100) = 15%

19. a.

b.

The highest price stock is for IBM with a price of $109 per share. The lowest price stock is for Alcoa with a price of $11 per share. A class size of 10 results in 10 classes. Price per Share $10–19

Frequency 5 2-11

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Cha pt e r2

$20–29 $30–39 $40–49 $50–59 $60–69 $70–79 $80–89 $90–99 $100–109

10 3 2 6 2 1 0 0 1

c.

Object36

The general shape of the distribution is skewed to the right. Half of the companies (15) have a price per share less than $30. A mid-priced stock appears to be in the $30 to $49 range, while the most frequently priced stock is in the $20 to $29 range. Five stocks are less than $20 per share (Alcoa, Bank of America, General Electric, Intel and Pfizer). Four stocks are $60 or more per share (3M, Chevron, ExxonMobil and IBM). 2-12 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

De s c r i pt i v eSt a t i s t i c s :Ta bul a ra ndGr a p hi c a lDi s pl a y s

d.

20. a.

A variety of comparisons are possible depending upon when the study is done.

Lowest = 12, Highest = 23

b. Percent Freque ncy

Hours in Meetings per Week

Freque ncy

11-12

1

4%

13-14

2

8%

15-16

6

24%

17-18

3

12%

19-20

5

20%

21-22

4

16%

23-24

4

16%

25

100%

c.

Object39

The distribution is slightly skewed to the left. 21. a / b/ c / d.

Revenue 0-49 50-99 100-149 150-199 200-249

Frequency 6 29 11 0 1

Relative Frequency .12 .58 .22 .00 .02

Cumulative Frequency 6 35 46 46 47

Cumulative Relative Frequency .12 .70 .92 .92 .94

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Cha pt e r2

250-299 1 .02 48 .96 300-349 0 .00 48 .96 350-399 0 .00 48 .96 400-449 2 .04 50 1.00 Total 50 1.00 e . Th ema j or i t yoft hel a r g ec or por a t i ons( 40)ha v er e v e nue si nt he$50bi l l i ont o$149bi l l i onr a n ge . Onl y4c or por a t i onsha v er e v e nue sofo v e r$200bi l l i ona n donl y2c or por a t i onsha v er e v e nue so v e r $400bi l l i on.. 70,or70%,oft hec or por a t i onsha v er e v e nue sunde r$100bi l l i on.. 30,or30%, oft he c or por a t i onsha v er e v e n ue sof$100bi l l i onormor e . f .

Object41

The histogram shows the distribution is skewed to the right with four corporations in the $200 to $449 billion range. g.

Exxon-Mobil is America’s largest corporation with an annual revenue of $443 billion. Walmart is the second largest corporation with an annual revenue of $406 billion. All other corporations have annual revenues less than $300 billion. Most (92%) have annual revenues less than $150 billion.

22. a.

b.

# U.S. Locations

Frequen cy

Percent Frequen cy

0-4999

10

50

5000-9999

3

15

10000-14999

2

10

15000-19999

1

5

20000-24999

0

0

25000-29999

1

5

30000-34999

2

10

35000-39999

1

5

Total: 20Rights Reserved. 100 © 2010 Cengage Learning. All May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

De s c r i pt i v eSt a t i s t i c s :Ta bul a ra ndGr a p hi c a lDi s pl a y s

Object44

c.

The distribution is skewed to the right. The majority of the franchises in this list have fewer than 20,000 locations (50% + 15% + 15% = 80%). McDonald's, Subway and 7-Eleven have the highest number of locations.

23. a/b. Co mput e r Us a g e( Hour s ) 0. 0 – 2. 9 3. 0 – 5. 9 6. 0 – 8. 9 9. 0 – 11. 9 12. 0 – 14. 9 Tot a l

Fr e que nc y 5 28 8 6 3 50

Re l a t i v e Fr e que nc y 0. 10 0. 56 0. 16 0. 12 0. 06 1. 00

c .

Object47

d . Thema j or i t yoft hec omp ut e rus e r sa r ei nt he3t o6h ourr a n g e .Us a g ei ss ome wha ts k e we dt o wa r d t her i ghtwi t h3us e r si nt he12t o14. 9ho urr a n g e .

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Cha pt e r2

24.

Me di a nPa y 6

677

7

2467789

8

00137

9

9

10 0 6 11 0 12 1 Theme d i a np a yf ort he s ec a r e e r si sg e n e r a l l yi nt he$ 70a nd$ 80t hous a nd s .Onl yf ourc a r e e r sh a v ea me di a npa yof$100t hous a ndormor e .Thehi ghe s tme di a npa yi s$121t hous a n df orafina nc e di r e c t or . TopPa y 10 0 6 9 11 1 6 9 12 2 5 6 13 0 5 8 8 14 0 6 15 2 5 7 16 17 18 19 20 21 4 22 1 Themos tf r e que ntt opp a yi si nt he$130t hous a n dr a n g e .Ho we v e r ,t het oppa yi sr a t he re v e nl y di s t r i but e dbe t we e n$100a nd$16 0t hous a n d.Twou nus ua l l yh i ght oppa yva l ue soc c ura t$214 t hous a ndf orafin a nc edi r e c t ora nd$221t hous a ndf ora ni n v e s t me ntba nk e r .Al s o,no t et ha tt het op pa yha smor ev a r i a bi l i t yt ha nt heme di a np a y .

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De s c r i pt i v eSt a t i s t i c s :Ta bul a ra ndGr a p hi c a lDi s pl a y s

25. 9 89 10 2 4 6 6 11 4 5 7 8 8 9 12 2 4 5 7 13 1 2 14 4 15 1 26.a . 2

14

2

67

3

011123

3

5677

4

003333344

4

6679

5

00022

5

5679

6

14

6

6

7

2

b . Most frequent age group: 40-44 with 9 runners c.

43 was the most frequent age with 5 runners

27.a . y

x

1

2

Tot a l

A

5

0

5

B

11

2

13

C

2

10

12

18

12

30

Tot a l

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Cha pt e r2

b . y

x

1

2

Tot a l

A

100. 0

0. 0

100. 0

B

84. 6

15. 4

100. 0

C

16. 7

...