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Levine Chapter 2
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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%
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
88 Chapter 2: Presenting Data in Tables and Charts 2.2 (b) cont.
Pie Chart
A12%
B29%
C35%
D24%
(c)
0%
5%
10%
15%
20%
25%
30%
35%
40%
C B D A
Category
%
0%10%20%30%40%50%60%70%80%90%100%
Cum
mul
ativ
e %
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%
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
MSN-Microsoft
Other
Yahoo
Sour
ce
Pareto Diagram
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
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%
80%
90%
100%
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
LTi
mer
War
ner
MSN
-M
icro
soft
Oth
er
Ask
Jeev
es
Source
0%10%20%30%40%50%60%70%80%90%100%
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%
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%
10%
20%
30%
40%
50%
60%
Coa
l
Nuc
lear
Nat
ural
gas
Hyd
ropo
wer Oil
Oth
er
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.
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.
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%
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%
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
ial
acco
mm
odat
ions
Reason
0%10%20%30%40%50%60%70%80%90%100%
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.
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
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.
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
0
2
4
6
8
10
12
14
90 110 130 150 170 190 210
Midpoints
Freq
uenc
y
Monthly Electricity Costs
Percentage Polygon
0%
5%
10%
15%
20%
25%
30%
70 90 110 130 150 170 190 210 230
Monthly Electricity Costs
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%
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
0.00
325
0.00
475
Midpoints
Freq
uenc
y
Percentage Polygon
0%
5%
10%
15%
20%
25%
30%
35%
-0.0
0425
-0.0
0275
-0.0
0125
0.00
025
0.00
175
0.00
325
0.00
475
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%
Solutions to End-of-Section and Chapter Review Problems 105 2.24 (b) cont.
Histogram
0
5
10
15
20
8.32
0
8.34
0
8.36
0
8.38
0
8.40
0
8.42
0
8.44
0
8.46
0
8.48
0
8.50
0
Midpoints
Freq
uenc
y
Percentage Polygon
0%
5%
10%
15%
20%
25%
30%
35%
8.30
8.32
8.34
8.36
8.38
8.40
8.42
8.44
8.46
8.48
8.50
8.52
(c)
Cumulative Percentage Polygon
0%
20%
40%
60%
80%
100%
120%
8.30
9
8.32
9
8.34
9
8.36
9
8.38
9
8.40
9
8.42
9
8.44
9
8.46
9
8.48
9
8.50
9
8.52
9
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
0
2
4
6
8
1525 1575 1625 1675 1725 1775 1825 1875
Midpoints
Freq
uenc
y
Percentage Polygon
0%
5%
10%
15%
20%
25%
1475
1525
1575
1625
1675
1725
1775
1825
1875
1925
Solutions to End-of-Section and Chapter Review Problems 107 2.25 (c) cont.
Cumulative Percentage Polygon
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1449
1499
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
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
ge
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
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
0
20
40
60
80
10065
0
750
850
950
1050
1150
1250
Life (Hours)
Perc
enta
ge
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
110 Chapter 2: Presenting Data in Tables and Charts 2.27 (b) cont.
Histogram
0
5
10
15
20
1.875 1.925 1.975 2.025 2.075 2.125
Amout of Soft Drink
Freq
uenc
y
Percentage Polygon
0
10
20
30
40
1.825 1.875 1.925 1.975 2.025 2.075 2.125 2.175
Mid-points
Perc
enta
ge
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
0
20
40
60
80
100
1.85 1.9 1.95 2 2.05 2.1 2.15
Amount of Soft Drink
Perc
enta
ge
(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%
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
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.
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.
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.
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
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.
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
$)
(b) Annual sales appear to be increasing in the earlier years before 1994 but start to
decline after 1998.
Solutions to End-of-Section and Chapter Review Problems 119 2.38 (a)
Scatter Plot
0
200
400
600
800
1000
1200
0 10 20 30 40 50
Energy Cost($)
Price
($)
(b) There does not appear to be any relationship between price and energy cost. (c) The data do not seem to indicate that higher-priced refrigerators have greater energy
efficiency.
2.39 (a)
Scatter Plot
05
101520253035
0 100 200 300 400 500
Turnover Rate
Viol
atio
ns
(b) There appears to be a negative relationship between the turnover rate and security
violations.
120 Chapter 2: Presenting Data in Tables and Charts 2.40 (a)
(b) There does not appear to be any relationship between the battery capacity and the digital-mode talk time.
(c) No, the data do not support the expectation that higher battery capacity is associated with higher talk time.
2.41 (a)
(b) There appears to be a positive relationship between cold-cranking amps and price. (c) Yes, the data seem to support the expectation that higher cranking amps are
associated with higher prices.
Scatter Plot
0.0
1.0
2.0
3.0
4.0
5.0
0 500 1000 1500 2000
Battery Capacity (milliampere-hours)
Talk
Tim
e (h
ours
)
Scatter Plot
020406080
100120140160
0 200 400 600 800 1000
Cold-cranking am ps
Pric
e ($
)
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.
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.
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
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
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.
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
%
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%
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.
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%
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
%
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%
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.
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
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%
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
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
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%
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.
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%
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
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
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.
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
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
umon
ia
Alz
heim
er's
dis
ease
Mot
or v
ehic
le a
ccid
ents
Suic
ide
Alc
ohol
-indu
ced
deal
ths
Emph
ysem
a
Dru
g-re
late
d de
aths HIV
Falls
Ass
ault
by fi
rear
ms
Ass
ault
by n
on-fi
rear
ms
Inju
ries
at w
ork
Ast
hma
Acc
iden
tal D
row
ning
Smok
e an
d Fi
re
Cause
0%10%20%30%40%50%60%70%80%90%100%
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
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".
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.
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%
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%
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.
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%
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.