Solucionario Estadistica

67
86 Chapter 2: Presenting Data in Tables and Charts CHAPTER 2 2.1 (a) Category Frequency Percentage A 13 26% B 28 56 C 9 18 (b) The Bar Chart 18% 56% 26% 0% 10% 20% 30% 40% 50% 60% C B A Percentage of Category (c) The Pie Chart C 18% B 56% A 26%

description

Levine Chapter 2

Transcript of Solucionario Estadistica

Page 1: Solucionario Estadistica

86 Chapter 2: Presenting Data in Tables and Charts

CHAPTER 2 2.1 (a) Category Frequency Percentage A 13 26% B 28 56 C 9 18 (b) The Bar Chart

18%

56%

26%

0% 10% 20% 30% 40% 50% 60%

C

B

A

Percentage of Category (c) The Pie Chart

C18%

B56%

A26%

Page 2: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 87 2.1 (d) cont. The Pareto diagram:

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

B A C

2.2 (a)

P erc en tag e

1 2

2 9

3 5

2 4

0 1 0 2 0 3 0 4 0

A

B

C

D

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88 Chapter 2: Presenting Data in Tables and Charts 2.2 (b) cont.

Pie Chart

A12%

B29%

C35%

D24%

(c)

0%

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35%

40%

C B D A

Category

%

0%10%20%30%40%50%60%70%80%90%100%

Cum

mul

ativ

e %

Page 4: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 89 2.3 (a)

Bar Chart

0 5 10 15 20 25 30 35 40 45 50

Lack of eye contact

Limited enthusiasm

Little or no knowledge of company

Other reasons

Unprepared to discuss career plans

Unprepared to discussskills/experience

Rea

son

Pie Chart

Lack of eye contact5%

Limited enthusiasm16%

Little or no knowledge of company

44%

Other reasons9%

Unprepared to discuss career plans23%

Unprepared to discuss skills/experience

3%

Page 5: Solucionario Estadistica

90 Chapter 2: Presenting Data in Tables and Charts 2.3 (a) cont.

(b) The Pareto diagram is better than the pie chart to portray these data because it not only sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale.

(c) From the Pareto diagram, it is obvious that “little or no knowledge of company” has constituted 44% of the most common mistake candidates make during job interviews. Therefore, it will be the mistakes you might try hardest to avoid. *

* Note: This is one of the many possible solutions for the question. 2.4 (a)

Bar Chart

0 5 10 15 20 25 30 35

AOL Timer Warner

Ask Jeeves

Google

MSN-Microsoft

Other

Yahoo

Sour

ce

Pareto Diagram

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45%

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Little or no knowledgeof company

Unprepared to discusscareer plans

Limited enthusiasm Other reasons Lack of eye contact Unprepared to discussskills/experience

Reason

0%

10%

20%

30%

40%

50%

60%

70%

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100%

Page 6: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 91 2.4 (a) cont.

Pie Chart

AOL Timer Warner

19%

Ask Jeeves3%

Google32%

MSN-Microsoft

15%

Other6%

Yahoo25%

Pareto Diagram

0%5%

10%15%20%25%30%35%

Goo

gle

Yaho

o

AO

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mer

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MSN

-M

icro

soft

Oth

er

Ask

Jeev

es

Source

0%10%20%30%40%50%60%70%80%90%100%

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92 Chapter 2: Presenting Data in Tables and Charts 2.4 (b) The Pareto diagram is better than the pie chart to portray these data because it not cont. only sorts the frequencies in descending order, it also provides the cumulative

polygon on the same scale. From the Pareto diagram, it is obvious that “Google” has the largest market share at 32%.*

* Note: This is one of the many possible solutions for the question. 2.5 (a)

Bar Chart

0 5 10 15 20 25 30

AmericanExpress

Discover

MasterCard

Visa

Cre

dit C

ard

$Billions

Pie Chart

AmericanExpress15.6%

Discover3.8%

MasterCard30.2%

Visa50.4%

Page 8: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 93 2.5 (a) cont.

Pareto Diagram

0%10%20%30%40%50%60%

Visa M asterCard AmericanExpress

Discover

Credit Card

0%

20%

40%

60%

80%

100%

(b) The Pareto diagram is better than the pie chart or the bar chart because it not only

sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale. From the Pareto diagram, it is obvious that more than 90% of the transactions were carried out with Visa, MasterCard and American Express credit cards. *

* Note: This is one of the many possible solutions for the question.

2.6 (a)

Pareto Diagram

0%

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Coa

l

Nuc

lear

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gas

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ropo

wer Oil

Oth

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Source

0%10%20%30%40%50%60%70%80%90%100%

(b) Approximately 88% of the electricity is derived from coal, nuclear energy or natural

gas.

Page 9: Solucionario Estadistica

94 Chapter 2: Presenting Data in Tables and Charts 2.6 (c) cont.

Pie Chart

Coal51%

Hydropower6%

Natural gas16%

Nuclear21%

Oil3%

Other3%

(d) The Pareto diagram is better than the pie chart because it not only sorts the

frequencies in descending order, it also provides the cumulative polygon on the same scale. From the Pareto diagram, it is obvious that almost 90% of the electricity is derived from coal, nuclear energy or natural gas. *

* Note: This is one of the many possible solutions for the question.

Page 10: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 95 2.7 (a)

Bar Chart

0 10 20 30 40 50

Don't know

Not work for pay at all

Other

Start own business

Work full-time

Work part-time

Plan

s

%

Pie Chart

Don't know3%

Not work for pay at all

29%

Other 5%

Start own business10%Work full-time

7%

Work part-time46%

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96 Chapter 2: Presenting Data in Tables and Charts 2.7 (b) The bar chart is more suitable if the purpose is to compare the categories. The

pie chart is more suitable if the main objective is to investigate the portion of the whole that is in a particular category. *

* Note: This is one of the many possible solutions for the question. 2.8 (a)

Bar Chart

0 10 20 30 40 50 60 70

Don't plan forsoftware

Have softwarefor all users

Have softwarefor some users

Plan for softwarein the next 12

months

Com

pany

Use

of A

nti-S

pam

Sof

twar

e

%

Pie Chart

Don't plan for software

9%

Have software for all users

59%

Have software for some users

12%

Plan for software in the next 12 months

20%

Page 12: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 97 2.8 (b) The bar chart is more suitable if the purpose is to compare the categories. The pie cont. chart is more suitable if the main objective is to investigate the portion of the

whole that is in a particular category. *

* Note: This is one of the many possible solutions for the question. 2.9 (a)

The Pareto Chart

0.000.100.200.300.400.50

Serv

er o

utof

mem

ory

Serv

erso

ftwar

e

Pow

erfa

ilure

Serv

erha

rdw

are

Phys

ical

conn

ectio

n

Inad

equa

teba

ndw

idth

Reason for Failure

%

0.000.200.400.600.801.00

Cum

. %

(b) The "vital few" reasons for the root causes of network crashes are "server out of memory" and "Server software" while the remaining reasons are the "trivial many" reasons.

2.10 (a)

Pareto Diagram

0%5%

10%15%20%25%30%35%

Roo

m d

irty

Roo

m n

eeds

mai

nten

ance

Roo

m n

otst

ocke

d

Roo

m n

ot re

ady

Roo

m to

o no

isy

Roo

m h

as to

ofe

w b

eds

Roo

m d

oesn

'tha

ve p

rom

ised

feat

ures

No

spec

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acco

mm

odat

ions

Reason

0%10%20%30%40%50%60%70%80%90%100%

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98 Chapter 2: Presenting Data in Tables and Charts 2.10 (b) The most frequent complain is about “room being dirty” followed by “room needs cont. maintenance” and “room not stocked”. The remaining complaints are the “trivial

many” reasons. 2.11 Ordered array: 63 64 68 71 75 88 94 2.12 Stem-and-leaf of Finance Scores 5 34 6 9 7 4 8 0 9 38 n = 7 2.13 Ordered array: 73 78 78 78 85 88 91 2.14 Ordered array: 50 74 74 76 81 89 92 2.15 (a) Ordered array: 9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2

(b) The stem-and-leaf display conveys more information than the ordered array. We can more readily determine the arrangement of the data from the stem-and-leaf display than we can from the ordered array. We can also obtain a sense of the distribution of the data from the stem-and-leaf display.

(c) The most likely gasoline purchase is between 11 and 11.9 gallons. (d) Yes, the third row is the most frequently occurring stem in the display and it is located in

the center of the distribution. 2.16 (a) Ordered array: $15 $15 $18 $18 $20 $20 $20 $20 $20 $21 $22 $22 $25 $25

$25 $25 $25 $26 $28 $29 $30 $30 $30 (b) PHStat output:

Stem-and-Leaf Display for Bounced-Check Fee Stem unit: 10

1 5 5 8 8 2 0 0 0 0 0 1 2 2 5 5 5 5 5 6 8 9 3 0 0 0

(c) The stem-and-leaf display provides more information because it not only orders observations from the smallest to the largest into stems and leaves, it also conveys information on how the values distribute and cluster over the range of the observations in the data set.

(d) The bounced checked fees seem to be concentrated around $22 which is the center of the 20-row and also the median of the 23 observations.

Page 14: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 99 2.17 (a) 0 0 5 5 5 5 5 5 6 6 6 7 7 7 8 8 9 9 9 10 10 10 10 10 12 12

(b) Excel output:

0 0 0 1 2 3 4 5 0 0 0 0 0 0 6 0 0 0 7 0 0 0 8 0 0 9 0 0 0

10 0 0 0 0 0 11 12 0 0

(c) The stem-and-leaf display provides more information because it not only orders observations from the smallest to the largest into stems and leaves, it also conveys information on how the values distribute and cluster over the range of the observations in the data set.

(d) The monthly service fees seem to be concentrated around 7 dollars, which is the median monthly service fee of the 26 observations, since 22 banks have service fees between 5 and 10 dollars. Or alternatively, the monthly service fees seem to be concentrated around 5 dollars and around 10 dollars, since 11 banks have service fees of 5 or10 dollars

2.18 (a) Ordered array for chicken: 7, 9, 15, 16, 16, 18, 22, 25, 27, 33, 39

Ordered array for burger: 19, 31, 34, 35, 39, 39, 43 (b) PHStat output:

(c) The stem-and-leaf display provides more information because it not only orders observations from the smallest to the largest into stems and leaves, it also conveys information on how the values distribute and cluster over the range of the observations in the data set.

(d) There seems to be higher fat content for burgers because 6 observations in the sample of 7 have fat content higher than 30 as compared to only 2 observations in the sample of 11 chicken items. Also, there is only 1 observation with a fat content lower than 20 for burgers as compared to 6 observations in the sample of 11 chicken items.

Stem-and-Leaf Displayfor BurgerStem unit: 10

1 923 1 4 5 9 94 3

Stem-and-Leaf Displayfor ChickenStem unit: 10

0 7 91 5 6 6 82 2 5 73 3 9

Page 15: Solucionario Estadistica

100 Chapter 2: Presenting Data in Tables and Charts 2.19 (a) Hotel: 117, 128, 128, 132, 145, 158, 159, 165, 177, 179, 180, 185, 198, 204, 205,

205, 210, 221, 269, 283 Car: 32, 32, 34, 38, 39, 40, 40, 41, 41, 41, 41, 46, 47, 48, 49, 49, 50, 56, 67, 69 (b) PHStat output: Hotel:

Stem-and-Leaf Display

Stem unit: 10

11 7 12 8 8 13 2 14 5 15 8 9 16 5 17 7 9 18 0 5 19 8 20 4 5 5 21 0 22 1 23242526 9 2728 3

Car:

Stem-and-Leaf Display

Stem unit: 10

3 2 2 4 8 9 4 0 0 1 1 1 1 6 7 8 9 9 5 0 6 6 7 9

(c) The stem-and-leaf display provides more information because it not only orders

observations from the smallest to the largest into stems and leaves, it also conveys information on how the values distribute and cluster over the range of the observations in the data set.

(d) Rental car cost is concentrated between $40 and $49 while hotel cost spread quite evenly from $120 to $220.

Page 16: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 101 2.20 (a) The class boundaries of the 9 classes can be "10 to less than 20", "20 to less than 30",

"30 to less than 40", "40 to less than 50", "50 to less than 60", "60 to less than 70", "70 to less than 80", "80 to less than 90", and "90 to less than 100".

(b) The class-interval width is 97.8 11.6 9.58 10

9−

= = ≅ .

(c) The nine class midpoints are: 15, 25, 35, 45, 55, 65, 75, 85, and 95. 2.21 (a) 4% (b) 32% (c) 36% (d) 100% 2.22 (a) Electricity Costs Frequency Percentage $80 up to $99 4 8% $100 up to $119 7 14 $120 up to $139 9 18 $140 up to $159 13 26 $160 up to $179 9 18 $180 up to $199 5 10 $200 up to $219 3 6 (b)

Histogram

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y

Monthly Electricity Costs

Percentage Polygon

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70 90 110 130 150 170 190 210 230

Monthly Electricity Costs

Page 17: Solucionario Estadistica

102 Chapter 2: Presenting Data in Tables and Charts 2.22 (c) cont.

Electricity Costs Frequency Percentage Cumulative %

$99 4 8% 8% $119 7 14% 22% $139 9 18% 40% $159 13 26% 66% $179 9 18% 84% $199 5 10% 94% $219 3 6% 100%

Cumulative Percentage Polygon

0%10%20%30%40%50%60%70%80%90%

100%

79 99 119 139 159 179 199 219 239

(d) Monthly electricity costs are most concentrated between $140 and $160 a month, with better than one-fourth of the costs falling in that interval.

2.23 (a)

Error Frequency Cumulative % Percentage-0.00350 -- -0.00201 13 13% 13%-0.00200 -- -0.00051 26 39% 26%-0.00050 -- 0.00099 32 71% 32%0.00100 -- 0.00249 20 91% 20%0.00250 -- 0.00399 8 99% 8%0.00400 -- 0.00549 1 100% 1%

Page 18: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 103 2.23 (b) cont.

Histogram

05

101520253035

-0.0

0275

-0.0

0125

0.00

025

0.00

175

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475

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uenc

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Percentage Polygon

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-0.0

0425

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025

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175

0.00

325

0.00

475

Page 19: Solucionario Estadistica

104 Chapter 2: Presenting Data in Tables and Charts 2.23 (c) cont.

Cumulative Percentage Polygon

0%10%20%30%40%50%60%70%80%90%

100%

-0.0

0351

-0.0

0201

-0.0

0051

0.00

099

0.00

249

0.00

399

0.00

549

(e) Yes, the steel mill is doing a good job at meeting the requirement as there is only one

steel part out of a sample of 100 that is as much as 0.005 inches longer than the specified requirement.

2.24 (a)

Width Frequency Percentage 8.310 -- 8.329 3 6.12%8.330 -- 8.349 2 4.08%8.350 -- 8.369 1 2.04%8.370 -- 8.389 4 8.16%8.390 -- 8.409 4 8.16%8.410 -- 8.429 15 30.61%8.430 -- 8.449 7 14.29%8.450 -- 8.469 5 10.20%8.470 -- 8.489 5 10.20%8.490 -- 8.509 3 6.12%

Page 20: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 105 2.24 (b) cont.

Histogram

0

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(c)

Cumulative Percentage Polygon

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Page 21: Solucionario Estadistica

106 Chapter 2: Presenting Data in Tables and Charts 2.24 (d) All the troughs will meet the company’s requirements of between 8.31 and 8.61 cont. inches wide. 2.25 (a)

Strength Frequency Percentage 1500 -- 1549 1 3.33%1550 -- 1599 2 6.67%1600 -- 1649 2 6.67%1650 -- 1699 7 23.33%1700 -- 1749 5 16.67%1750 -- 1799 7 23.33%1800 -- 1849 3 10.00%1850 -- 1899 3 10.00%

(b)

Histogram

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1925

Page 22: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 107 2.25 (c) cont.

Cumulative Percentage Polygon

0%

10%

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50%

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1449

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1549

1599

1649

1699

1749

1799

1849

1899

1949

(d) The strength of all the insulators meets the company’s requirement of at least 1500.

2.26 (a)

Bulb Life (hrs) Frequency Manufacturer A

Bulb Life (hrs) Frequency Manufacturer B

650 -- 749 3 750 -- 849 2 750 -- 849 5 850 -- 949 8 850 -- 949 20 950 -- 1049 16

950 -- 1049 9 1050 -- 1149 9 1050 -- 1149 3 1150 -- 1249 5

Percentage, Percentage, Bulb Life (hrs) Mfgr A Mfgr B

650 – 749 7.5% 0.0% 750 – 849 12.5 5.0 850 – 949 50.0 20.0 950 – 1049 22.5 40.0 1050 – 1149 7.5 22.5 1150 – 1249 0.0 12.5

Page 23: Solucionario Estadistica

108 Chapter 2: Presenting Data in Tables and Charts 2.26 (b) cont.

Percentage Histogram (Manufacturer A)

0102030405060

749 849 949 1049 1149 1249

Bin

Perc

enta

ge

Percentage Histogram (Manufacturer B)

01020304050

749 849 949 1049 1149 1249

Bin

Perc

enta

ge

Percentage Polygon

0102030405060

600 700 800 900 1000 1100 1200

Mid-points

Perc

enta

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Manufacturer AManufacturer B

(c) Frequency Frequency Less Than, Less Than, Bulb Life (hrs) Mfgr A Mfgr B

650 – 749 3 0 750 – 849 8 2 850 – 949 28 10 950 – 1049 37 26 1050 – 1149 40 35 1150 – 1249 40 40

Page 24: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 109 2.26 (c) Percentage Percentage cont. Less Than, Less Than, Bulb Life (hrs) Mfgr A Mfgr B

650 – 749 7.5% 0.0% 750 – 849 20.0 5.0 850 – 949 70.0 25.0 950 – 1049 92.5 65.0 1050 – 1149 100.0 87.5 1150 – 1249 100.0 100.0

Ogives

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Manufacturer AManufacturer B

(d) Manufacturer B produces bulbs with longer lives than Manufacturer A. The

cumulative percentage for Manufacturer B shows 65% of their bulbs lasted 1049 hours or less contrasted with 70% of Manufacturer A’s bulbs which lasted 949 hours or less. None of Manufacturer A’s bulbs lasted more than 1149 hours, but 12.5% of Manufacturer B’s bulbs lasted between 1150 and 1249 hours. At the same time, 7.5% of Manufacturer A’s bulbs lasted less than 750 hours, while all of Manufacturer B’s bulbs lasted at least 750 hours.

2.27 (a) Amount of

Soft Drink Frequency Percentage 1.850 – 1.899 1 2% 1.900 – 1.949 5 10 1.950 – 1.999 18 36 2.000 – 2.049 19 38 2.050 – 2.099 6 12 2.100 – 2.149 1 2

Page 25: Solucionario Estadistica

110 Chapter 2: Presenting Data in Tables and Charts 2.27 (b) cont.

Histogram

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Percentage Polygon

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Mid-points

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Page 26: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 111 2.27 (c) Amount of Frequency Percentage cont. Soft Drink Less Than Less Than

1.85 – 1.89 1 2% 1.90 – 1.94 6 12 1.95 – 1.99 24 48 2.00 – 2.04 43 86 2.05 – 2.09 49 98 2.10 – 2.14 50 100

Cumulative Percentage Polygon

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1.85 1.9 1.95 2 2.05 2.1 2.15

Amount of Soft Drink

Perc

enta

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(d) The amount of soft drink filled in the two liter bottles is most concentrated in two

intervals on either side of the two-liter mark, from 1.950 to 1.999 and from 2.000 to 2.049 liters. Almost three-fourths of the 50 bottles sampled contained between 1.950 liters and 2.049 liters.

2.28 (a) Table frequencies for all student responses Student Major Categories Gender A C M Totals Male 14 9 2 25 Female 6 6 3 15 Totals 20 15 5 40 (b) Table percentages based on overall student responses Student Major Categories Gender A C M Totals Male 35.0% 22.5% 5.0% 62.5% Female 15.0% 15.0% 7.5% 37.5% Totals 50.0% 37.5% 12.5% 100.0% Table based on row percentages Student Major Categories Gender A C M Totals Male 56.0% 36.0% 8.0% 100.0% Female 40.0% 40.0% 20.0% 100.0% Totals 50.0% 37.5% 12.5% 100.0% Table based on column percentages Student Major Categories Gender A C M Totals Male 70.0% 60.0% 40.0% 62.5% Female 30.0% 40.0% 60.0% 37.5% Totals 100.0% 100.0% 100.0% 100.0%

Page 27: Solucionario Estadistica

112 Chapter 2: Presenting Data in Tables and Charts 2.28 (c) cont.

0 2 4 6 8 10 12 14

A

C

R

MaleFemale

2.29

Side-by-side Bar Chart

0 20 40 60 80 100

1

2

3

Col

umn

Cat

egor

ies

BA

Page 28: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 113 2.30 (a) Contingency Table

Condition of Die Quality No Particles Particles Totals Good 320 14 334Bad 80 36 116Totals 400 50 450

Table of Total Percentages Condition of Die Quality No Particles Particles Totals Good 71% 3% 74%Bad 18% 8% 26%Totals 89% 11% 100%

Table of Row Percentages

Condition of Die Quality No Particles Particles Totals Good 96% 4% 100%Bad 69% 31% 100%Totals 89% 11% 100%

Table of Column Percentages Condition of Die Quality No Particles Particles Totals Good 80% 28% 74%Bad 20% 72% 26%Totals 100% 100% 100%

(b)

Side-by-side Bar Chart

320

14

80

36

0 100 200 300 400

No Particles

Particles

Con

ditio

n of

Die

Frequency

BadGood

(c) The data suggests that there is some association between condition of the die and the quality of wafer because more good wafers are produced when no particles are found

in the die and more bad wafers are produced when there are particles found in the die.

Page 29: Solucionario Estadistica

114 Chapter 2: Presenting Data in Tables and Charts 2.31 (a)

Table of total percentages

Day EveningNonconforming 1.6% 2.4% 4%Conforming 65.4% 30.6% 96%Total 67% 33% 100%

Shift

Table of row percentages

Day EveningNonconforming 40% 60% 100%Conforming 68% 32% 100%Total 67% 33% 100%

Shift

Table of column percentages

Day EveningNonconforming 2% 7% 4%Conforming 98% 93% 96%Total 100% 100% 100%

Shift

(b) The row percentages allow us to block the effect of disproportionate group size and show us that the pattern for day and evening tests among the nonconforming group is very different from the pattern for day and evening tests among the conforming group. Where 40% of the nonconforming group was tested during the day, 68% of the conforming group was tested during the day.

(c) The director of the lab may be able to cut the number of nonconforming tests by reducing the number of tests run in the evening, when there is a higher percent of tests run improperly.

Page 30: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 115 2.32 (a) Table of total percentages

Gender Enjoy Shopping for Clothing

Male Female Total

Yes 27% 45% 72% No 21% 7% 28% Total 48% 52% 100%

Table of row percentages

Gender Enjoy Shopping for Clothing

Male Female Total

Yes 38% 62% 100% No 74% 26% 100% Total 48% 52% 100%

Table of column percentages

Gender Enjoy Shopping for Clothing

Male Female Total

Yes 57% 86% 72% No 43% 14% 28% Total 100% 100% 100%

(b)

Side-by-side Bar Chart

0 100 200 300

Male

Female

Gen

der

Frequency

NoYes

(c) The percentage of shoppers who enjoy shopping for clothing is higher among females than males.

Page 31: Solucionario Estadistica

116 Chapter 2: Presenting Data in Tables and Charts 2.33 (a) Column percentages:

Total Sales in Millions $ Apparel Company

April 2001 April 2002

Gap 31.00% 25.09%TJX 20.91% 23.45%Limited 15.95% 16.18%Kohl's 14.57% 17.71%Nordstrom 10.77% 10.91%Talbots 3.74% 3.39%AnnTaylor 3.05% 3.26%Total 100.00% 100.00%

(b)

(c) In general, retail sales for the apparel industry have seen a modest growth between April 2001 and April 2002 with the exception of Talbots, whose sales have declined slightly and Gap, whose sales have declined by almost 200 million dollars.

Side-by-side Bar Chart

0 500 1000 1500

Gap

TJX

Lim ited

Kohl's

Nordstrom

Talbots

AnnTaylor

App

arel

Com

pany

Total Sales (m illions $)

April 2002April 2001

Page 32: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 117 2.34 (a)

Side-by-side Bar Chart

0 2000 4000 6000

Buick

Chevrolet

Chrysler

Ford

Lincoln

Bra

nd

Frequency

20032001

(b) All five brands increased the amount of rebates from 2001 to 2003 with Ford more

than doubling, Chevrolet and Buick almost doubling the amount of rebates. 2.35 (a)

Side-by-side Bar Chart

0 100,000 200,000 300,000 400,000

Nissan

Honda

Toyota

Chrysler

Ford

GM

Car

Mak

er

Frequency

20042003

(b) All car makers except Ford experienced an increase in sales of new cars and light

trucks from January 2003 to January 2004.

Page 33: Solucionario Estadistica

118 Chapter 2: Presenting Data in Tables and Charts 2.36 (a)

Scatter Plot

0

10

20

30

40

50

60

0 5 10 15 20

X

Y

(b) Yes, there appears to be a positive linear relationship between X and Y.

2.37 (a)

Time Series Plot

0

5

10

15

20

25

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Year

Sale

s (in

mill

ions

of c

onst

ant

1995

$)

(b) Annual sales appear to be increasing in the earlier years before 1994 but start to

decline after 1998.

Page 34: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 119 2.38 (a)

Scatter Plot

0

200

400

600

800

1000

1200

0 10 20 30 40 50

Energy Cost($)

Price

($)

(b) There does not appear to be any relationship between price and energy cost. (c) The data do not seem to indicate that higher-priced refrigerators have greater energy

efficiency.

2.39 (a)

Scatter Plot

05

101520253035

0 100 200 300 400 500

Turnover Rate

Viol

atio

ns

(b) There appears to be a negative relationship between the turnover rate and security

violations.

Page 35: Solucionario Estadistica

120 Chapter 2: Presenting Data in Tables and Charts 2.40 (a)

(b) There does not appear to be any relationship between the battery capacity and the digital-mode talk time.

(c) No, the data do not support the expectation that higher battery capacity is associated with higher talk time.

2.41 (a)

(b) There appears to be a positive relationship between cold-cranking amps and price. (c) Yes, the data seem to support the expectation that higher cranking amps are

associated with higher prices.

Scatter Plot

0.0

1.0

2.0

3.0

4.0

5.0

0 500 1000 1500 2000

Battery Capacity (milliampere-hours)

Talk

Tim

e (h

ours

)

Scatter Plot

020406080

100120140160

0 200 400 600 800 1000

Cold-cranking am ps

Pric

e ($

)

Page 36: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 121 2.42 (a)

Unemployment Rate

01234567

1998

Jan

uary

Apr

il

July

Oct

ober

1999

Jan

uary

Apr

il

July

Oct

ober

2000

Jan

uary

Apr

il

July

Oct

ober

2001

Jan

uary

Apr

il

July

Oct

ober

2002

Jan

uary

Apr

il

July

Oct

ober

2003

Jan

uary

Apr

il

July

Oct

ober

(b) The unemployment rate followed a downward trend from January of 1998 to

September of 2000 and changed to an upward trend from there onwards. 2.43 (a)

1.85

1.9

1.95

2

2.05

2.1

2.15

0 20 40 60Bottle Number

Am

ount

(lite

rs)

(b) There is a downward trend in the amount filled. (c) The amount filled in next bottle will most likely be below 1.894 liter. (d) The scatter plot of the amount of soft drink filled against time reveals the trend of the

data while a histogram only provides information on the distribution of the data.

Page 37: Solucionario Estadistica

122 Chapter 2: Presenting Data in Tables and Charts 2.44 (a)

Number of Households (millions)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

1994 1996 1998 2000 2002 2004

(b) There is an upward trend in the number of households using online banking and/or online bill payment.

(c) The number of U.S. households actively using online banking and/or online bill payment in 2004 will be around 36 millions.

2.45 (a)

Scatter Plot

0.0

5.0

10.0

15.0

20.0

25.0

1994 1996 1998 2000 2002 2004

Year

View

ers

Per G

ame

(in

mill

ions

) NFLNBAMLBNHL

(b) There is a steady decline in the number of television viewers for the NBA

after 1997. The MLB experienced a sharp decline in television viewers from 1995 to 1996 but the number of viewers remained rather steady from there onwards. The number of television viewers for the NFL and NHL remained quite steady from 1995 to 2002.

(c) The television viewers for the NFL, NBA, MLB and NHL will probably be around 18 million, 4 million, 8 million, and 2.9 million, respectively.

Page 38: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 123 2.49 (a) Good features: (1) the length of the lightning is proportional to the number of

fatalities; (2) the years are labeled chronologically from left to right. (b) Bad features: (1) the background graphic is an example of chartjunk; (2) the shading

in the background reduces the data-ink ratio and does not convey any valuable information.

2.50 (a) The size of the policeman for Washington is not only taller but also bigger in overall

size. This has a tendency to distort the actual difference in the size of the police forces. A simple bar chart would do a much better job.

2.51 (a) Good features: (1) the bar chart used is an appropriate graphical tool for the

categorical data; (2) the x-axis is properly labeled. (b) Bad features: (1) the background graphic complicates the presentation of the data and

distracts viewers attention from the real data; (2) the y-axis is not labeled. 2.53 (a)

Doughnut Chart of Percentage (%)

ComparisonshoppingConvenience

Free shipping

Larger selection

Speed

05

101520253035

Perc

enta

ge

Com

paris

onsh

oppi

ng

Con

veni

ence

Free

ship

ping

Larg

erse

lect

ion

Spee

d

Reason

Cone Chart

Page 39: Solucionario Estadistica

124 Chapter 2: Presenting Data in Tables and Charts 2.53 (a) cont.

05

101520253035

Perc

enta

ge

Com

paris

onsh

oppi

ng

Con

veni

ence

Free

ship

ping

Larg

erse

lect

ion

Spe

ed

Reason

Pyramid Chart

(b) The bar chart, the pie chart and the Pareto diagram should be preferred over the

doughnut chart, the cone chart and the pyramid chart since the former set is simpler and easier to interpret.

2.54 (a)

Doughnut Chart for the Percentage of Funds %

LowAverage High

Page 40: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 125 2.54 (a) cont.

0

10

20

30

40

50

60

Num

ber o

f Fun

ds

Low Average High

Fund Risk Level

Cone Chart

0

10

20

30

40

50

60

Num

ber o

f Fun

ds

Low Average High

Fund Risk Level

Pyramid Chart

(b) The bar chart, the pie chart and the Pareto diagram should be preferred over the

doughnut chart, the cone chart and the pyramid chart since the former set is simpler and easier to interpret.

2.55 A histogram uses bars to represent each class while a polygon uses a single point. The

histogram should be used for only one group, while several polygons can be plotted on a single graph.

2.56 A summary table allows one to determine the frequency or percentage of occurrences in each

category.

Page 41: Solucionario Estadistica

126 Chapter 2: Presenting Data in Tables and Charts 2.57 A bar chart is useful for comparing categories. A pie chart is useful when examining the

portion of the whole that is in each category. A Pareto diagram is useful in focusing on the categories that make up most of the frequencies or percentages.

2.58 The bar chart for categorical data is plotted with the categories on the vertical axis and the

frequencies or percentages on the horizontal axis. In addition, there is a separation between categories. The histogram is plotted with the class grouping on the horizontal axis and the frequencies or percentages on the vertical axis. This allows one to more easily determine the distribution of the data. In addition, there are no gaps between classes in the histogram.

2.59 A time-series plot is a type of scatter diagram with time on the x-axis. 2.60 Because the categories are arranged according to frequency or importance, it allows the user

to focus attention on the categories that have the greatest frequency or importance. 2.61 Percentage breakdowns according to the total percentage, the row percentage, and/or the

column percentage allow the interpretation of data in a two-way contingency table from several different perspectives.

2.62 (a)

Bar Chart

0 10 20 30 40 50 60 70

Author

Bookstore

Freight

Publisher

Rev

enue

Cat

egor

ies

%

Page 42: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 127 2.62 (a) cont.

Pie Chart

Author11.6%

Bookstore22.4%

Freight1.2%

Publisher64.8%

Pareto Diagram

0%

10%

20%

30%

40%

50%

60%

70%

Publisher Bookstore Author Freight

Revenue Categories

0%10%20%30%40%50%60%70%80%90%100%

Page 43: Solucionario Estadistica

128 Chapter 2: Presenting Data in Tables and Charts 2.62 (b) cont.

Pareto Diagram

0%

5%

10%

15%

20%

25%

30%

35%M

anuf

actu

ring

cost

s

Mar

ketin

g an

dpr

omot

ion

Aut

hor

Empl

oyee

sala

ries

and

bene

fits

Adm

inis

trat

ive

cost

s an

dta

xes

Afte

r-ta

x pr

ofit

Ope

ratio

ns

Pret

ax p

rofit

Frei

ght

Revenue Categories

0%10%20%30%40%50%60%70%80%90%100%

(c) The publisher gets the largest portion (64.8%) of the revenue. About half (32.2%) of

the revenue received by the publisher is used for manufacturing costs. Bookstore marketing and promotion account for the next larger share of the revenue at 15.4%. Author, bookstore employee salaries and benefits, and publisher administrative costs and taxes each accounts for around 10% of the revenue while the publisher after-tax profit, bookstore operations, bookstore pretax profit and freight constitute the “trivial few” allocations of the revenue.

Page 44: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 129 2.63 (a)

Bar Chart (1992 %)

0 10 20 30 40 50

Foreign specialists

Others

Parts stores with service bays

Repair specialists

Service stations, garages

Tire stores

Vehicle dealers

Sour

ce

%

Pie Chart (1992 %)

Foreign specialists 3.9%

Others 7.3%

Parts stores with service bays

7.3%

Repair specialists 12.7%

Service stations, garages39.1%

Tire stores 8.1%

Vehicle dealers 21.6%

Page 45: Solucionario Estadistica

130 Chapter 2: Presenting Data in Tables and Charts 2.63 (a) cont.

Pareto Diagram (1992 %)

0%5%

10%15%20%25%30%35%40%45%

Serv

ice

stat

ions

,ga

rage

s

Vehi

cle

deal

ers

Rep

air

spec

ialis

ts

Tire

sto

res

Oth

ers

Part

s st

ores

with

ser

vice

bays

Fore

ign

spec

ialis

ts

Source

0%10%20%30%40%50%60%70%80%90%100%

Bar Chart (2002 %)

0 5 10 15 20 25 30 35

Foreign specialists

Others

Parts stores with service bays

Repair specialists

Service stations, garages

Tire stores

Vehicle dealers

Sour

ce

%

Page 46: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 131 2.63 (a) cont.

Pie Chart (2002 %)

Foreign specialists 6.0%

Others 6.4%

Parts stores with service bays

6.4%

Repair specialists 16.2%

Service stations, garages29.5%

Tire stores 8.9%

Vehicle dealers 26.6%

Pareto Diagram (2002%)

0%

5%

10%

15%

20%

25%

30%

35%

Serv

ice

stat

ions

,ga

rage

s

Vehi

cle

deal

ers

Rep

air

spec

ialis

ts

Tire

sto

res

Oth

ers

Part

s st

ores

with

ser

vice

bays

Fore

ign

spec

ialis

ts

Source

0%10%20%30%40%50%60%70%80%90%100%

Page 47: Solucionario Estadistica

132 Chapter 2: Presenting Data in Tables and Charts 2.63 (b) cont.

Side-by-side Bar Chart

0 10 20 30 40 50

Foreign specialists

Parts stores with service bays

Repair specialists

Service stations, garages

Tire stores

Vehicle dealers

Others So

urce

%

2002%1992%

(c) Vehicle dealers, tire stores, repair specialists and foreign specialists gained market

share between 1992 and 2002 while parts stores with service bays, service stations and garages, and others lost market share.

2.64 (a)

Side-by-Side Bar Chart

0 20 40 60

Cash

Check

Debit

Credit

Other

Type

of P

aym

ent

%

2003%2001%1999%

(b) From 1999 to 2003, payment by cash and check had declined while payment by debit

and other type of payment had increased. The percentage of payment by credit had remained more or less constant.

Page 48: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 133 2.65 (a)

Type of Drink 1998 2000 2002Bottled water 3.92% 6.28% 9.87%Dairy/other 0.47% 0.46% 0.44%Juice/drinks 4.87% 5.67% 5.89%Soft drinks 84.77% 81.16% 77.32%Sports drinks 2.98% 3.37% 3.68%Tea 2.98% 3.06% 2.80%Total 100.00% 100.00% 100.00%

(b)

Bar Chart (1998)

0 10 20 30 40 50 60

Bottled water

Dairy/other

Juice/drinks

Soft drinks

Sports drinks

Tea

Type

of D

rink

Frequency

Page 49: Solucionario Estadistica

134 Chapter 2: Presenting Data in Tables and Charts 2.65 (b) cont.

Pie Chart (1998)

Bottled waterDairy/other Juice/drinks Soft drinks Sports drinks Tea

Pareto Diagram (1998)

0%10%20%30%40%50%60%70%80%90%

Soft

drin

ks

Juic

e/dr

inks

Bot

tled

wat

er

Spor

tsdr

inks

Tea

Dai

ry/o

ther

Type of Drink

75%

80%

85%

90%

95%

100%

Page 50: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 135 2.65 (b) cont.

Bar Chart (2000)

0 10 20 30 40 50 60

Bottled water

Dairy/other

Juice/drinks

Soft drinks

Sports drinks

Tea Ty

pe o

f Drin

k

Frequency

Pie Chart

Bottled waterDairy/other Juice/drinks Soft drinks Sports drinks Tea

Page 51: Solucionario Estadistica

136 Chapter 2: Presenting Data in Tables and Charts 2.65 (b) cont.

Pareto Diagram (2000)

0%10%20%30%40%50%60%70%80%90%

Soft

drin

ks

Bot

tled

wat

er

Juic

e/dr

inks

Spor

tsdr

inks

Tea

Dai

ry/o

ther

Type of Drink

0%10%20%30%40%50%60%70%80%90%100%

Bar Chart (2002)

0 10 20 30 40 50 60

Bottled water

Dairy/other

Juice/drinks

Soft drinks

Sports drinks

Tea

Type

of D

rink

Frequency

Page 52: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 137 2.65 (b) cont.

Pie Chart (2002)

Bottled waterDairy/other Juice/drinks Soft drinks Sports drinks Tea

Pareto Diagram (2002)

0%10%20%30%40%50%60%70%80%90%

Soft

drin

ks

Bot

tled

wat

er

Juic

e/dr

inks

Spor

tsdr

inks

Tea

Dai

ry/o

ther

Type of Drink

0%10%20%30%40%50%60%70%80%90%100%

Page 53: Solucionario Estadistica

138 Chapter 2: Presenting Data in Tables and Charts 2.65 (c) Note: Since the range of the percentages for soft drinks is much larger than that of the

remaining types of beverages, including soft drinks in the same side-by-side chart with the rest will visually obscure the information of the remaining beverages. We, therefore, provide two separate side-by-side bar charts, one with just soft drinks alone and another without soft drinks.

Side-by-side bar chart without soft drinks:

Side-by-side Bar Chart

0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%

Bottled water

Dairy/other

Juice/drinks

Sports drinks

Tea

Type

of D

rink

%

200220001998

Side-by-side bar chart for soft drinks:

Side-by-Side Bar Chart

72.00%

74.00%

76.00%

78.00%

80.00%

82.00%

84.00%

86.00%

Soft drinks

Type

of D

rink

%

200220001998

(d) Sports drinks, juice/drinks and especially bottled water experienced an increase in

market share from 1998 to 2002 while soft drinks suffered a decline in market share. The market share of dairy/other and tea remained pretty constant over the period.

Page 54: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 139 2.66 (a)

The Pareto diagram is most appropriate because it not only sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale. From the Pareto diagram, it is obvious that USA and Brazil make up more than half of the coffee consumption in major markets in 2000.

(b)

Pareto Diagram for Leading Coffee Brands in Brazil

0%10%20%30%40%50%60%70%

All

Oth

ers

Sara

Lee

owne

dbr

ands

Nes

cafe

Tres

Cor

acoe

s

Mel

itta

Brand

0%10%20%30%40%50%60%70%80%90%100%

The Pareto diagram is most appropriate because it not only sorts the frequencies in

descending order, it also provides the cumulative polygon on the same scale. From the Pareto diagram, it is obvious that no single major corporation dominates the coffee market in Brazil. The corporation that owns the largest share of the market, Sara Lee owned brands, captures only less than 30% of the market share.

Pareto Diagram for Coffee Consumption in Major Markets in 2000

0%5%

10%15%20%25%30%35%40%

USA

Bra

zil

Ger

man

y

Japa

n

Fran

ce

Net

herla

nds

Finl

and

County

0%10%20%30%40%50%60%70%80%90%100%

Page 55: Solucionario Estadistica

140 Chapter 2: Presenting Data in Tables and Charts 2.67 (a)

Bar Chart

0 50 100 150 200 250 300

AlgeriaAngola

BrazilBritain

CanadaChinaIndia

IndonesiaIranIraq

KazakhstanKuwait

LibyaMexicoNigeriaNorway

OmanOther Africa

Other Central and South AmericaOther Eastern Europe and

Other Far East and OceaniaOther Middle East

Other Western EuropeQatar

RussiaSaudi Arabia

U.S.United Arab Emirates

Venezuela

Cou

ntrie

s

Pie ChartAlgeriaAngolaBrazilBritainCanadaChinaIndiaIndonesiaIranIraqKazakhstanKuwaitLibyaMexicoNigeriaNorwayOmanOther AfricaOther Central and South AmericaOther Eastern Europe and former USSROther Far East and OceaniaOther Middle EastOther Western EuropeQatarRussiaSaudi ArabiaU.S.United Arab EmiratesVenezuela

Page 56: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 141 2.67 (a) cont.

Pareto Diagram

0%

5%

10%

15%

20%

25%

30%Sa

udi A

rabi

a

Iraq

Uni

ted

Ara

b Em

irate

s

Kuw

ait

Iran

Vene

zuel

a

Rus

sia

Liby

a

Mex

ico

Chi

na

Nig

eria

U.S

.

Qat

ar

Oth

er M

iddl

e Ea

st

Oth

er F

ar E

ast a

nd O

cean

iaO

ther

Cen

tral

and

Sou

thA

mer

ica

Nor

way

Alg

eria

Oth

er A

fric

a

Bra

zil

Om

an

Ang

ola

Kaz

akhs

tan

Brit

ain

Indo

nesi

aO

ther

Eas

tern

Eur

ope

and

form

er U

SSR C

anad

a

Indi

a

Oth

er W

este

rn E

urop

e

Countries

0%10%20%30%40%50%60%70%80%90%100%

(b)

Bar Chart

0 200 400 600 800

Africa

Central and South America

Eastern Europe and FormerUSSR

Far East and Oceania

Middle East

North America

Western Europe

Reg

ion

Page 57: Solucionario Estadistica

142 Chapter 2: Presenting Data in Tables and Charts 2.67 (b) cont.

Pie Chart

Africa7% Central and South

America9%

Eastern Europe and Former USSR

6%

Far East and Oceania4%

Middle East67%

North America5%

Western Europe2%

Pareto Diagram

0%10%20%30%40%50%60%70%

Mid

dle

East

Cen

tral

and

Sou

thA

mer

ica A

fric

a

East

ern

Euro

pean

d Fo

rmer

USS

R

Nor

th A

mer

ica

Far E

ast a

ndO

cean

ia

Wes

tern

Eur

ope

Region

0%10%20%30%40%50%60%70%80%90%100%

(c) The Pareto diagram is most appropriate because it not only sorts the frequencies in

descending order, it also provides the cumulative polygon on the same scale. (d) The Middle East, with a share of more than 60%, obviously has the largest proven

conventional reserves. Among the set of countries, Saudi Arabia has the largest share of proven conventional reserves followed by Iraq, United Arab Emirates and Kuwait. These four countries account for more than half of the reserves among the set of countries.

Page 58: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 143 2.68 (a)

There is no particular pattern to the deaths due to terrorism on U.S. soil between 1990 and 2001. There are exceptionally high death counts in 1995 and 2001 due to the Okalahoma City and New York City bombings.

(b)

Scatter Diagram

0

500

1000

1500

2000

2500

3000

1988 1990 1992 1994 1996 1998 2000 2002

Year

Dea

ths

Bar Chart

0 100 200 300 400 500 600 700 800

Accidental DrowningAlcohol-induced dealths

Alzheimer's diseaseAssault by firearms

Assault by non-firearmsAsthmaCancer

DiabetesDrug-related deaths

EmphysemaFalls

Heart diseasesHIV

Influenza and pneumoniaInjuries at work

Motor vehicle accidentsSmoke and Fire

Strokes and related diseasesSuicide

Cau

se

Page 59: Solucionario Estadistica

144 Chapter 2: Presenting Data in Tables and Charts 2.68 (b) cont.

Pie Chart

0%1%3%1%0%0%

31%

4%1%

1%1%

40%

1%4%

0%2%

0%9%

2% Accidental DrowningAlcohol-induced dealthsAlzheimer's diseaseAssault by firearmsAssault by non-firearmsAsthmaCancerDiabetesDrug-related deathsEmphysemaFallsHeart diseasesHIVInfluenza and pneumoniaInjuries at workMotor vehicle accidentsSmoke and FireStrokes and related diseasesSuicide

Pareto Diagram

0%5%

10%15%20%25%30%35%40%45%

Hea

rt d

isea

ses

Can

cer

Stro

kes

and

rela

ted

dise

ases Dia

bete

s

Influ

enza

and

pne

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Page 60: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 145 2.68 (c) The Pareto diagram is best to portray these data because it not only sorts the cont. frequencies in descending order, it also provides the cumulative polygon on the same

scale. The labels in the pie chart are unreadable because there are too many categories in the causes of death.

(d) The major causes of death in the U.S. in 2000 are heart diseases followed by cancer. These two accounted for more than 70% of the total deaths.

2.69 (a)

Type of Entrée Number Served % Beef 187 31.2% Chicken 103 17.2% Duck 25 4.2% Fish 122 20.3% Pasta 63 10.5% Shellfish 74 12.3% Veal 26 4.3% Total 600 100.0%

(b) Bar Chart

0 20 40 60 80 100 120 140 160 180 200

Beef

Chicken

Duck

Fish

Pasta

Shellfish

Veal

Type

Page 61: Solucionario Estadistica

146 Chapter 2: Presenting Data in Tables and Charts 2.69 (b) cont.

Pie Chart

Beef

Chicken

Duck

Fish

Pasta

Shellfish

Veal

Pareto Diagram

0%

5%

10%

15%

20%

25%

30%

35%

Beef Fish Chicken Shellfish Pasta Veal DuckType

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

(c) The Pareto diagram has the advantage of offering the cumulative percentage view of

the categories and, hence, enables the viewer to separate the "vital few" from the "trivial many".

Page 62: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 147 2.69 (d) Beef and fish account for more than 50% of all entrees ordered by weekend patrons cont. of a continental restaurant. When chicken is included, better than two-thirds of the

entrees are accounted for. 2.70 (a) Table of row percentages

Gender Beef Entrée Dessert Ordered Male Female Total Dessert Ordered Yes No Total Yes 71% 29% 100% Yes 52% 48% 100%No 48% 52% 100% No 25% 75% 100%Total 53% 47% 100% Total 31% 69% 100%

Table of column percentages Gender Beef Entrée Dessert Ordered Male Female Total Dessert Ordered Yes No Total Yes 30% 14% 23% Yes 38% 16% 23%No 70% 86% 77% No 62% 84% 77%Total 100% 100% 100% Total 100% 100% 100%

Table of total percentages Gender Beef Entrée Dessert Ordered Male Female Total Dessert Ordered Yes No Total Yes 16% 7% 23% Yes 12% 11% 23%No 37% 40% 77% No 19% 58% 77%Total 53% 47% 100% Total 31% 69% 100%

(b) If the owner is interested in finding out the percentage of joint occurrence of gender

and ordering of dessert or the percentage of joint occurrence of ordering a beef entrée and a dessert among all patrons, the table of total percentages is most informative. If the owner is interested in the effect of gender on ordering of dessert or the effect of ordering a beef entrée on the ordering of dessert, the table of column percentages will be most informative. Since dessert will usually be ordered after the main entree and the owner has no direct control over the gender of patrons, the table of row percentages is not very useful here.

(c) 30% of the men sampled ordered desserts compared to 14% of the women. Men are more than twice as likely to order desserts as women. Almost 38% of the patrons ordering a beef entree ordered dessert compared to less than 16% of patrons ordering all other entrees. Patrons ordering beef are better than 2.3 times as likely to order dessert as patrons ordering any other entree.

Page 63: Solucionario Estadistica

148 Chapter 2: Presenting Data in Tables and Charts 2.71 (a)

Counties Pie Chart (1980)

Electronic0%

LeverMachines

37%

Mixed3%

Optical Scan1%

Paper Ballots40%

Punch Cards19%

Counties Pie Chart (2000)

Electronic9%

LeverMachines

14%Mixed

4%

Optical Scan42%

Paper Ballots12%

Punch Cards19%

Counties Pie Chart (2002)

Electronic16%

LeverMachines

11%Mixed

4%

Optical Scan42%

Paper Ballots11%

Punch Cards16%

Page 64: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 149 2.71 (a) cont.

Registered Voters Pie Chart (1980)

Electronic1%

LeverMachines

42%

Mixed12%

Optical Scan2%

Paper Ballots11%

Punch Cards32%

Registered Voters Pie Chart (2000)

Electronic12%

LeverMachines

17%

Mixed7%

Optical Scan31%

Paper Ballots2%

Punch Cards31%

Registered Voters Pie Chart (2002)

Electronic20%

LeverMachines

15%

Mixed9%

Optical Scan32%

Paper Ballots1%

Punch Cards23%

Page 65: Solucionario Estadistica

150 Chapter 2: Presenting Data in Tables and Charts 2.71 (b) cont.

Counties Side-by-side Chart

0 10 20 30 40 50

Punch Cards

Lever Machines

Paper Ballots

Optical Scan

Electronic

Mixed

Meth

od

%

200220001980

Registered Voters Side-by-side Chart

0 10 20 30 40 50

Punch Cards

Lever Machines

Paper Ballots

Optical Scan

Electronic

Mixed

Meth

od

%

200220001980

(c) When performing comparison between two data sets, the side-by-side bar chart is

more helpful. (d) The pattern in methods used in the counties and the registered voters is fairly similar

with a few exceptions. In the counties, the percentage using mixed methods is the lowest in 1980 while the percentage using mixed methods is the lowest in 2000 for registered voters. For the counties the use of paper ballots dropped from around 40% in 1980 to around 15% in 2000, an approximate 60% drop, while the drop in paper ballots used among registered voters was from around 10% in 1980 to around 1.5% in 2000, an approximate 85% drop.

Page 66: Solucionario Estadistica

Solutions to End-of-Section and Chapter Review Problems 151 2.72 (a)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

23575R15 311050R15 30950R15 23570R15 Others 331250R15 25570R16

Tire Size

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

23575R15 accounts for over 80% of the warranty claims.

(b)

Tread separation accounts for the majority (70%) of the warranty claims.

Pie Chart

Blow out6%

Other/Unknown24%

Tread Separation70%

Page 67: Solucionario Estadistica

152 Chapter 2: Presenting Data in Tables and Charts 2.72 (c) cont.

0%

10%

20%

30%

40%

50%

60%

70%

80%

Tread Separation Other/Unknown Blow Out

Incident for ATX Model

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Tread separation accounts for more than 70% of the warranty claims among the ATX

model. (d)

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Other/Unknown Tread Separation Blow Out

Incident for Wilderness Model

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

The number of claims is quite evenly distributed among the three incidents. The

incident of “other/unknown” accounts for almost 40% of the claims, the incident of “tread separation” accounts for about 35% of the claims while the incident of “blow out” accounts for about 25% of the claims.