Preview Extract

Chapter 2
11
Chapter 2
Organizing and Graphing Data
Section 2.1
2.1
Data in their original form are often too large and unmanageable. It is easier to make sense of grouped data
than ungrouped data and easier to make decisions and draw conclusions using grouped data.
2.2
The relative frequency for a category is obtained by dividing the frequency of that category by the sum of
the frequencies of all categories. The percentage for a category is obtained by multiplying the relative
frequency of that category by 100. Example 2๏ญ2 in the text is an example which shows how relative
frequencies and percentages are calculated.
2.3
a. and b.
Category
Frequency
Y
N
D
23
13
4
Relative
Frequency
23/40 = 0.575
13/40 = 0.325
4/40 = 0.100
c. 57.5% of the elements belong to category Y.
d. 17/40 = 42.5% of the elements belong to categories N or D.
e.
D
10.0%
N
32.5%
Y
57.5%
Percentage
57.5
32.5
10.0
Chapter 2
f.
Pareto Chart of Categories
40
100
Counts
60
20
Percent
80
30
40
10
a. and b.
0
Categories
Counts
Percent
Cum %
Y
23
57.5
57.5
Category
Frequency
G
B
I
14
21
5
N
13
32.5
90.0
D
0
4
10.0
100.0
Relative
Frequency
14/40 = 0.35
21/40 = 0.525
5/40 = 0.125
Percentage
35
52.5
12.5
c. Thirty-five percent of the adults in this sample said that building casinos is good.
d. (21 + 5) / 40 = 65% of the adults in this sample either said that building casinos is bad or were
indifferent.
e.
Chart of Counts
20
15
Counts
2.4
20
10
5
0
B
G
Categories
I
12
Chapter 2
f.
Pie Chart of Categories
Category
B
G
I
I 12.5%
G 35%
B 52.5%
g.
Pareto Chart of Categories
40
100
Counts
60
20
Percent
80
30
40
10
0
Categories
Counts
Percent
Cum %
2.5
a. and b.
c.
Category
PI
S
V
PO
B
C
20
G
21
52.5
52.5
B
14
35.0
87.5
Frequency
9
8
13
3
1
2
I
0
5
12.5
100.0
Relative Frequency
9/36 = 0.25
8/36 = 0.222
13/36 = 0.361
3/36 = 0.083
1/36 = 0.028
2/36 = 0.056
V + PO + C = 13 + 3 + 2 = 18; 18/36 = 0.5 = 50%
50% of the respondents mentioned vegetables and fruits, poultry, or cheese.
Percentage
25
22.2
36.1
8.3
2.8
5.6
13
Chapter 2
Relative Frequency
d.
0.4
0.3
0.2
0.1
0
PI
S
V
PO
B
C
Favorite Pizza Topping
2.6
a. and b.
Category
Frequency
C
CK
CC
D
O
4
5
4
2
1
c.
CC
25.0%
D
12.5%
O
6.3%
C
25.0%
CK
31.3%
Relative
Frequency
4/16 = 0.250
5/16 = 0.313
4/16 = 0.250
2/16 = 0.125
1/16 = 0.063
Percentage
25.0
31.3
25.0
12.5
6.3
14
Chapter 2
2.7
15
a. Let N = No financial stress, S = Some financial stress, H = High financial stress, and
O = Overwhelming financial stress.
Pie Chart of Financial Stress Level
Category
N
S
H
O
O
5% N 14%
H 18%
S 63%
b.
100
100
80
80
60
60
40
40
20
20
0
Financial Stress Level
Percentage
Percent
Cum %
S
63
63.0
63.0
H
18
18.0
81.0
N
14
14.0
95.0
Other
5
5.0
100.0
Percent
Percentage
Pareto Chart of Financial Stress Level
0
Section 2.2
2.8
The three decisions that have to be made to group a data set in the form of a frequency distribution table are
1. The number of classes to be used to group the given data.
2. The width of each class.
3. The lower limit of the first class.
2.9
The relative frequency for a class is obtained by dividing the frequency of that class by the sum of
frequencies of all classes. The percentage for a class is obtained by multiplying the relative frequency of
that class by 100. Example 2-4 is an example that illustrates the calculation of relative frequencies and
percentages.
2.10
A data set that does not contain fractional values is usually grouped by using classes with limits. Example
2๏ญ4 is an example of the writing classes using limits method. A data set that contains fractional values is
grouped by using the less than method. Example 2๏ญ5 is an example of the less than method. Single-valued
Chapter 2
16
classes are used to group a data set that contains only a few distinct (integer) values. Example 2๏ญ6 is an
example of the single-valued classes method.
2.11
a. 31 + 78 + 49 + 81 + 117 + 13 = 369 customers were served.
b. Each class has a width of 4.
Gallons of Gas
Class Width
(Class Limits)
0 to less than 4
4
4 to less than 8
4
8 to less than 12
4
12 to less than 16
4
16 to less than 20
4
20 to less than 24
4
Gallons of Gas
0 to less than 4
4 to less than 8
8 to less than 12
12 to less than 16
16 to less than 20
20 to less than 24
c.
Class Midpoint
0+4
=2
2
4+8
=6
2
8 + 12
= 10
2
12 + 16
= 14
2
16 + 20
= 18
2
20 + 24
= 22
2
Number of Customers
31
78
49
81
117
13
Relative Frequency
31/369 โ 0.084
78/369 โ 0.211
49/369 โ 0.133
81/369 โ 0.220
117/369 โ 0.317
13/369 โ 0.035
Percentage
8.4
21.1
13.3
22.0
31.7
3.5
d. 22.0 + 31.7 + 3.5 = 57.2% of the customers purchased 12 gallons or more.
e. The number of customers who purchased 10 gallons or less cannot be determined exactly because 10 is
not a boundary value.
f.
2.12
Gallons of Gasoline
Cumulative Frequency
0 to less than 4
0 to less than 8
0 to less than 12
0 to less than 16
0 to less than 20
0 to less than 24
31
31 + 78 = 109
31 + 78 + 49 = 158
31 + 78 + 49 + 81 = 239
31 + 78 + 49 + 81 + 117 = 356
31 + 78 + 49 + 81 + 117 + 13 = 369
a. and b.
Class Limits
$1 to $200
$201 to $400
$401 to $600
$601 to $800
$801 to $1000
$1001 to $1200
Cumulative
Relative Frequency
31/369 = 0.084
109/369 = 0.295
158/369 = 0.428
239/369 = 0.648
356/369 = 0.965
1.000
Class Boundaries
$0.5 to less than $200.5
$200.5 to less than $400.5
$400.5 to less than $600.5
$600.5 to less than $800.5
$800.5 to less than $1000.5
$1000.5 to less than $1200.5
Class Midpoints
$100.5
$300.5
$500.5
$700.5
$ 900.5
$1100.5
Cumulative
Percentage
8.4
29.5
42.8
64.8
96.5
100.0
Chapter 2
2.13
a. and b.
Commuting Times
Frequency
0 to 9
10 to 19
20 to 29
30 to 39
40 to 49
2
14
14
13
7
Relative
Frequency
2/50 = 0.04
14/50 = 0.28
14/50 = 0.28
13/50 = 0.26
7/50 = 0.14
17
Percentage
4
28
28
26
14
c.
Histogram for Commuting Times
30
25
Percentage
20
15
10
5
0
0 to 9
10 to 19
20 to 29
30 to 39
40 to 49
Commuting Times
d.
(13 + 7)/50 = 40% of the workers in the sample commute for 30 minutes or more.
e.
Commuting
Times
0 to 9
10 to 19
20 to 29
30 to 39
40 to 49
2.14
a. and b.
Cumulative Frequency
2
2 + 14 = 16
2 + 14 + 14 = 30
2 + 14 + 14 + 13 = 43
2 + 14 + 14 + 13 + 7 = 50
Age
20 to 29
30 to 39
40 to 49
50 to 59
60 to 69
Cumulative
Relative
Frequency
2/50 = 0.04
16/50 = 0.32
30/50 = 0.60
43/50 = 0.86
50/50 = 1.00
Frequency
6
9
6
8
1
Cumulative
Percentage
4
32
60
86
100
Relative Frequency
6/30 = 0.200
9/30 = 0.300
6/30 = 0.200
8/30 = 0.267
1/30 = 0.033
Percentage
20.0
30.0
20.0
26.7
3.30
Chapter 2
c.
Frequency Histogram for Age of Male Participants
9
8
Frequency
7
6
5
4
3
2
1
0
20 to 29
30 to 39
40 to 49
50 to 59
60 to 69
Age of Male Participants
d.
a. and b.
Age
20 to 29
30 to 39
40 to 49
50 to 59
60 to 69
Frequency
8
9
6
6
1
Relative Frequency
8/30 = 0.267
9/30 = 0.300
6/30 = 0.200
6/30 = 0.200
1/30 = 0.033
Percentage
26.7
30.0
20.0
20.0
3.30
c.
Frequency Histogram for Age of Female Participants
9
8
7
Frequency
2.15
(6 + 9)/30 = 50% of the male participants are younger than 40 years of age.
6
5
4
3
2
1
0
20 to 29
30 to 39
40 to 49
50 to 59
60 to 69
Age of Female Participants
d.
(8 + 9)/30 = 56.7% of female participants are younger than 40 years of age.
e.
The male and female age distributions are very similar, with only slight differences in the exact
heights of the bars.
18
Chapter 2
2.16
a. and b.
Weight
91 to 125
126 to 160
161 to 195
196 to 230
231 to 265
Frequency
2
7
5
10
6
Relative Frequency
2/30 = 0.067
7/30 = 0.233
5/30 = 0.167
10/30 = 0.333
6/30 = 0.200
Percentage
6.7
23.3
16.7
33.3
20.0
c.
Relative Frequency Histogram for Weights of Male Participants
0.35
Relative Frequency
0.30
0.25
0.20
0.15
0.10
0.05
0.00
91 to 125
126 to 160
161 to 195
196 to 230
231 to 265
Weights of Male Participants
d.
a. and b.
Weight
91 to 125
126 to 160
161 to 195
196 to 230
231 to 265
Frequency
5
7
3
6
9
Relative Frequency
5/30 = 0.167
7/30 = 0.233
3/30 = 0.100
6/30 = 0.200
9/30 = 0.300
c.
Relative Frequency Histogram for Weights of Female Participants
0.30
0.25
Relative Frequency
2.17
(2 + 7)/30 = 30% of male participants weighed less than 161 pounds.
0.20
0.15
0.10
0.05
0.00
91 to 125
126 to 160
161 to 195
196 to 230
231 to 265
Weights of Female Participants
d.
(5 + 7)/30 = 40% of female participants weighed less than 161 pounds.
Percentage
16.7
23.3
10.0
20.0
30.0
19
Chapter 2
e.
2.18
The weight distributions were similar, but 10% more of the females had a weight below 161 pounds
than did the males. The percentage above 195 pounds was the same in both distributions, but of these
more females fell in the 231 to 265 pounds range than did males.
a. and b.
Blood Glucose Level
75 to 89
90 to 104
105 to 119
120 to 134
135 to 149
Frequency
5
7
8
7
3
Relative Frequency
5/30 = 0.167
7/30 = 0.233
8/30 = 0.267
7/30 = 0.233
3/30 = 0.100
Percentage
16.7
23.3
26.7
23.3
10.0
c.
Percentage Distribution Histogram for Male Blood Glucose Levels
30
25
Percentage
20
15
10
5
0
75 to 89
90 to 104
105 to 119
120 to 134
135 to 149
Blood Glucose Level of Males
d.
(7 + 3)/30 = 33.3% of male participants had a blood glucose level higher than 119.
e.
Blood
Glucose
Level
75 to 89
75 to 104
75 to 119
75 to 134
75 to 149
2.19
20
Cumulative Frequency
Cumulative Relative
Frequency
Cumulative
Percentage
5
5 + 7 = 12
5 + 7 + 8 = 20
5 + 7 + 8 + 7 = 27
5 + 7 + 8 + 7 + 3 = 30
5/30 = 0.167
12/30 = 0.400
20/30 = 0.667
27/30 = 0.900
30/30 = 1.000
16.7
40.0
66.7
90.0
100.0
Relative Frequency
6/30 = 0.200
4/30 = 0.133
7/30 = 0.233
7/30 = 0.233
6/30 = 0.200
Percentage
20.0
13.3
23.3
23.3
20.0
a. and b.
Blood Glucose Level
75 to 89
90 to 104
105 to 119
120 to 134
135 to 149
Frequency
6
4
7
7
6
Chapter 2
c.
Percentage Distribution Histogram for Female Blood Glucose Levels
25
Percentage
20
15
10
5
0
75 to 89
90 to 104
105 to 119
120 to 134
135 to 149
Blood Glucose Level of Females
d.
(7 + 6)/30 = 43.3% of female participants had a blood glucose level higher than 119.
e. Taking the center of both distributions to be the class 105 to 119, the shape of the left and right tails
between the two distribution is swapped, meaning there are more females with blood glucose levels
less than 119 than there are males with such glucose levels, and there are more females with blood
glucose level greater than 119 than there are males with such blood glucose levels.
f.
Blood
Glucose
Level
75 to 89
75 to 104
75 to 119
75 to 134
75 to 149
Cumulative Frequency
6
6 + 4 = 10
6 + 4 + 7 = 17
6 + 4 + 7 + 7 = 24
6 +4 + 7 + 7 + 6 = 30
Cumulative
Relative
Frequency
6/30 = 0.200
10/30 = 0.333
17/30 = 0.567
24/30 = 0.800
30/30 = 1.000
Cumulative
Percentage
20.0
33.3
56.7
80.0
100.0
2.20
Strikeouts Per Game
6.30 to less than 6.85
6.85 to less than 7.40
7.40 to less than 7.95
7.95 to less than 8.50
8.50 to less than 9.05
Frequency
3
6
10
9
2
Relative Frequency
3/30 = 0.100
6/30 = 0.200
10/30 = 0.333
9/30 = 0.300
2/30 = 0.067
Percentage
10.0
20.0
33.3
30.0
6.7
21
Chapter 2
2.21
a. and b.
Turnovers
1
2
3
4
5
6
7
8
Frequency
4
5
3
3
7
2
0
1
Relative Frequency
4/25 = 0.160
5/25 = 0.200
3/25 = 0.120
3/25 = 0.120
7/25 = 0.280
2/25 = 0.080
0/25 = 0.000
1/25 = 0.040
22
Percentage
16.0
20.0
12.0
12.0
28.0
8.0
0.0
4.0
c. 3 + 7 = 10 games had four or five turnovers. The relative frequency is 10/25 = 0.400.
Frequency
d.
7
6
5
4
3
2
1
0
1
2
3
4
5
6
Turnovers
7
8
2.22
65
Frequency
Frequency
60
40
20
55
45
35
25
0
0
1
2
3
4
Number of Tickets
0
1
2
3
4
Number of Tickets
The truncated graph exaggerates the difference in the number of students with different numbers of tickets.
Section 2.3
2.23
To prepare a stem-and-leaf display for a data set, each value is divided into two parts; the first part is
called the stem and the second part is called the leaf. The stems are written on the left side of a vertical line
and the leaves for each stem are written on the right side of the vertical line next to the corresponding stem.
Example 2-9 is an example of a stem-and-leaf display.
2.24
The advantage of a stem-and-leaf display over a frequency distribution is that by preparing a stem-and-leaf
display we do not lose information on individual observations. From a stem-and-leaf display we can obtain
the original data. However, we cannot obtain the original data from a frequency distribution table. Consider
the stem-and-leaf display from Example 2๏ญ8:
5 2 0 7
6 5 9 1 8 4
7 5 9 1 2 6 9 7 1 2
8 0 7 1 6 3 4 7
9 6 3 5 2 2 8
Chapter 2
The data that were used to make this stem-and-leaf display are: 52, 50, 57, 65, 69, 61, 68, 64, 75, 79, 71,
72, 76, 79, 77, 71, 72, 80, 87, 81, 86, 83, 84, 87, 96, 93, 95, 92, 92, 98
2.25
The data that were used to make this stem-and-leaf display are: 218, 245, 256, 329, 367, 383, 397, 404,
427, 433, 471, 523, 537, 551, 563, 581, 592, 622, 636, 647, 655, 678, 689, 810, 841
23
Chapter 2
2.26
0
1
2
3
4
5
6
2.27
24
1
0
0
1
8
0
8
a.
b.
3
2
2
4
3
3
4
3
6
5
3
7
6
4
6
5
8
6
9
6
9
7
9
7
9
0
1
2
3
4
7
1
1
0
0
9
2
2
0
2
4
2
1
2
5
3
1
4
5
3
2
6
6
4
2
6
7
4
3
8
7
5
4
8
6
6
8
6
7
8
6
7
8
8
9
0
0
1
1
2
2
3
3
4
4
7
1
5
1
5
0
6
0
6
9
2
5
2
6
0
7
2
6
4
6
2
6
1
7
2
8
7
3
6
1
9
4
7
3
8
2
9
8
4
9
2
8
4
9
3
8
8
9
9
2
3
0
1
5
3 5 5 5 6 8 8 8 9
1 2 2 2 3 4 4 5 5 6 7 8 8 9
2 8
8
0
0
1
1
2
2
3
3
3
5
0
5
1
8
3
5
1
5
2
5
8
5
3
9
7
6
5
2
6
6
2
7
9
6
9
.
0
1
2
3
4
5
6
9
9
4
a. 0
1
2
3
b.
2.29
9
9
9
Answers will vary, but the split stem-and-leaf display seems to better discern differences in the data in
the range 10 โ 30.
c.
2.28
2
2
0
3
8
1
5
0
1
2
3
0
5
7
1
2
3
8
8
2
8
8
3
8
8
4
9
9
4
Chapter 2
2.30
a.
b.
25
2
3
4
5
6
7
8
9
2-4
5-6
7-9
58
20
30
05
10
02
40
57
58
05
02
45
38
30
17
05
45
68
*
30
05
60
38
20
06
68
20
38
06
90
50
35
20
70
60
38
21
90
45
50
20
*
60
21
65
70
75
28
65
87
30
65
28
38
70
65
60
75
87
90
*
*
10
40
17
45
20
68
35
70
38
90
*
57
68
Section 2.4
2.31
In order to prepare a dotplot, first we draw a horizontal line with numbers that cover the given data set.
Then we place a dot above the value on the number line that represents each measurement in the data set.
Example 2-12 illustrates this procedure.
2.32
The benefits of a dot plot is that it is quick to form and it can illustrate where data points in a set naturally
cluster.
2.33
2.34
Dotplot of Vehicle Fatalities
0
9
18
27
36
Vehicle Fatalities
2.35
45
54
63
Chapter 2
26
2.36
Dotplot of Scores
2.37
35
42
49
56
63
70
77
Scores
Supplementary Exercises
2.38
a. and b.
Political Party
D
DR
F
R
W
Frequency
9
4
2
11
4
Relative Frequency
9/30 = 0.300
4/30 = 0.133
2/30 = 0.067
11/30 = 0.367
4/30 = 0.133
Percentage
30.0
13.3
6.7
36.7
13.3
c.
Relative
Frequency
W
13.3%
D
30.0%
0.4
0.3
0.2
0.1
0
R
36.7%
D
DR
F
R
W
DR
13.3%
F
6.7%
Political Party
d. 13.3% of these presidents were Whigs.
2.39
a. and b.
TV sets owned
0
1
2
3
4
Frequency
1
14
14
8
3
Relative Frequency
1/40 = 0.025
14/40 = 0.350
14/40 = 0.350
8/40 = 0.200
3/40 = 0.075
Percentage
2.5
35.0
35.0
20.0
7.5
Chapter 2
27
c.
Frequency
15
10
5
0
0
1
2
3
4
TV Sets Owned
d. (14 + 8 + 3)/40 = 62.5% of the households own two or more television sets.
2.40
a. and b.
Number of Text Messages
32โ37
38โ43
44โ49
50โ55
56โ61
Frequency
10
9
13
6
2
Relative Frequency
10/40 = 0.250
9/40 = 0.225
13/40 = 0.325
6/40 = 0.150
2/40 = 0.050
Percentage
25.0
22.5
32.5
15.0
5.0
Percentage
c.
15
10
5
0
32-37 38-43 44-49 50-55 56-61
Number of Text Messages
d.
2.41
On (13 + 6 + 2)/40 = 52.5% of the 40 days, the student sent more than 44 text messages.
a. and b.
Number of Orders
23 โ 29
30 โ 36
37 โ 43
44 โ 50
51 โ 57
Frequency
4
9
6
8
3
Relative Frequency
4/30 = 0.133
9/30 = 0.300
6/30 = 0.200
8/30 = 0.267
3/30 = 0.100
Percentage
13.3
30.0
20.0
26.7
10.0
c. For (6 + 8 + 3)/30 = 56.7% of the hours in this sample, the number of orders was more than 36.
2.42
a. and b.
Concession (dollars)
0 to less than 6
6 to less than 12
12 to less than 18
18 to less than 24
24 to less than 30
Frequency
9
10
5
4
2
Relative Frequency
9/30 = 0.300
10/30 = 0.333
5/30 = 0.167
4/30 = 0.133
2/30 = 0.067
Percentage
30.0
33.3
16.7
13.3
6.7
Chapter 2
28
c.
Frequency
15
10
5
0
0-6
6 – 12 12 – 18 18 – 24 24 – 30
Concessions
a. and b.
2.43
Commute Length
(in minutes)
22 to less than 28
28 to less than 34
34 to less than 40
40 to less than 46
46 to less than 52
Frequency
Relative Frequency
Percentage
5
14
8
2
1
5/30 = 0.167
14/30 = 0.467
8/30 = 0.267
2/30 = 0.067
1/30 = 0.033
16.7
46.7
26.7
6.7
3.3
c.
Frequency Histogram for Commute Length
14
12
Frequency
10
8
6
4
2
0
22 to less than 28 28 to less than 34 34 to less than 40 40 to less than 46 46 to less than 52
Commute Length (in minutes)
2.44
2.45
3
4
5
6
2
0
0
1
2
3
4
5
3
1
0
3
1
1
4
2
2
4
0
1
0
5
2
3
7
0
1
2
6
2
4
7
3
9
7
1
4
3
7
4
7
4
7
5
8
2
5
7
8
5
3
6
9
5
7
7
4
7
4
7
2.47
20
30
40
Number of Orders
50
7
60
7
7
5
9
8
8
6
9
7
8
8
9
Chapter 2
2.48
29
Age
18 to less than 20
20 to less than 25
25 to less than 30
30 to less than 40
40 to less than 50
50 to less than 60
60 and over
a.
Frequency
7
12
18
14
15
16
35
Relative Frequency
7/117 = 0.060
12/117 = 0.103
18/117 = 0.154
14/117 = 0.120
15/117 = 0.128
16/117 = 0.137
35/117 = 0.299
Relative Frequency
.300
.250
.200
.150
.100
.050
60 and over
50 to < 60
40 to < 50
30 to < 40
25 to < 30
20 to < 25
18 to < 20
.000
b. and c. This histogram is misleading because the class widths differ. If you were to change the frequency
distribution so that the class widths were equal, the resulting histogram would give a clearer
picture.
2.49
a. Using Sturgeโs formula:
c = 1 + 3.3log n = 1 + 3.3log135
= 1 + 3.3(2.13033377)
= 1 + 7.03 = 8.03 ยป 8
.
b. Approximate class width
Largest value – smallest value
=
Number of classes
53 – 20
=
= 4.125
8
Use a class width of 5.
2.50
a.
The top money winners on the menโs tour tend to make more money per tournament than those on the
womenโs tour. Earnings on the menโs tour begin at $2300, and more of the data points are toward the
higher end of the scale. Earnings on the womenโs tour begin at $800, and more of the data points are
toward the lower end of the scale.
b. Typical earnings per tournament played for the womenโs tour would be around $2500; typical earnings
per tournament played for the menโs tour would be around $3650.
c.
The data do not appear to have similar spreads for the two tours. Earnings on the menโs tour begin at
$2300, the largest grouping is between $2300 and $4800, and go up to $9500. Earnings on the
womenโs tour begin at $800, the largest grouping is between $1100 and $2600, and only go up to
$7500.
Chapter 2
30
d. On the womenโs tour, the $7500 earnings level appears to be an outlier; on the menโs tour, both the
$8700 and $9500 earnings levels appear to be outliers.
a. Answers will vary.
2.51
b. i.
9
10
11
12
13
14
15
16
17
18
19
20
9
2
0
3
2
6
5
1
4
0
3
2
8
4
3
3
7
9
2
4
2
3
4
8
5
3
8
7
5
5
6
8
9
8
9
9
8
4
5
3
5
8
9
9
ii. The display shows a bimodal distribution, due to the presence of both females and males in the
sample. The males tend to be heavier, so their weights are concentrated in the larger values, while
the femalesโ weights are found primarily in the smaller values.
c.
Females
9
8
6
8
5
5
Males
8
5
3
8
4
3
6
7
9
2
0
3
3
8
5
4
9
10
11
12
13
14
15
16
17
18
19
20
2
7
9
1
4
0
3
2
8
2
4
2
3
4
8
5
3
5
9
9
9
9
Self-Review Test
1.
An ungrouped data set contains information on each member of a sample or population individually. The first
part of Example 2-1 in the text, listing the responses of each of the 30 employees, is an example of ungrouped
data. Data presented in the form of a frequency table are called grouped data. Table 2.4 in the solution of
Example 2-1 is an example of grouped data.
2. a. 5
b. 7
c. 17
d. 6.5
e. 13.5
f. 90
g. .30
3. A histogram that is identical on both sides of its central point is called a symmetric histogram. A histogram that
is skewed to the right has a longer tail on the right side, and a histogram that is skewed to the left has a longer
tail on the left side. Figure 2.8 in the text provides graphs of symmetric histograms, Figure 2.9a displays a
histogram skewed to the right, and Figure 2.9b displays a histogram that is skewed to the left.
Chapter 2
a. and b.
c.
Net Worth vs.
$200,000
M
L
N
Frequency
Relative Frequency
Percentage
12
18
6
12/36 = 0.333
18/36 = 0.500
6/36 = 0.167
33.3
50.0
16.7
18/36 = 50% of senior citizens have net worth less than $200,000.
d.
Frequency Histogram for Networth Classification
20
Frequency
15
10
5
0
M
L
N
Networth Classification
e.
Pareto Chart of Networth Classification
40
100
30
80
60
20
40
10
20
0
Networth Classification
Frequency
Percent
Cum %
L
18
50.0
50.0
M
12
33.3
83.3
N
6
16.7
100.0
0
Percent
Frequency
4.
31
Chapter 2
f.
Pie Chart of Networth Classification
Category
M
L
N
N 16.7%
M 33.3%
L 50%
5. a. and b.
Monthly Expense on Gas
(in dollars)
50 to 149
150 to 249
250 to 349
350 to 449
450 to 549
Frequency
Relative Frequency
Percentage
9
13
11
9
6
9/48 = 0.188
13/48 = 0.271
11/48 = 0.229
9/48 = 0.188
6/48 = 0.125
18.8
27.1
22.9
18.8
12.5
c.
Percentage Distribution Histogram for Monthly Expenses on Gas
30
25
Percentage
20
15
10
5
0
50 to 149
150 to 249
250 to 349
350 to 449
450 to 549
Monthly Expenses on Gas (in $)
d. (9 + 6)/48 = 31.25% of car owners in this sample spent $350 or more on gas per month.
e.
Monthly Expense
Cumulative
on Gas
Frequency
50 to 149
9
150 to 249
9 + 13 = 22
250 to 349
9 + 13 + 11 = 33
350 to 449
9 + 13 + 11 + 9 = 42
450 to 549
9 + 13 + 11 + 9 + 6 = 48
Shopping Expense
Frequency
Cumulative
Relative Frequency
9/48 = 0.188
22/48 = 0.458
33/48 = 0.688
42/48 = 0.875
48/48 = 1.000
Relative Frequency
Cumulative
Percentage
18.8
45.8
68.8
87.5
100.0
Percentage
32
Chapter 2
6. a. and c.
(in dollars)
20 to less than 60
60 to less than 100
100 to less than 140
140 to less than 180
180 to less than 220
6
8
7
5
4
6/30 = 0.200
8/30 = 0.267
7/30 = 0.233
5/30 = 0.167
4/30 = 0.133
20.0
26.7
23.3
16.7
13.3
b. The width of each class is 40 dollars.
d. (6 + 8 + 7)/30 = 70% of these customers spent less than $140 at this grocery store.
e.
Frequency Histogram for Shopping Expenses
9
8
Frequency
7
6
5
4
3
2
1
0
2o
to
ss
le
an
th
60
60
to
ss
le
an
th
0
10
0
10
to
ss
le
an
th
0
14
0
14
to
ss
le
an
th
0
18
0
18
to
ss
le
an
th
0
22
Shopping Expenses (in $)
Shopping Expense
(in dollars)
20 to less than 60
60 to less than 100
100 to less than 140
140 to less than 180
180 to less than 220
f.
7.
8.
9.
0
1
2
3
4
0
0
2
30
6
2
1
7
2
2
8
3
2
4
5
4
9
5
6
Cumulative
Frequency
6
6 + 8 = 14
6 + 8 + 7 = 21
6 + 8 + 7 + 5 = 26
6 + 8 + 7 + 5 + 4 = 30
6
6
7
8
Cumulative
Relative Frequency
6/30 = 0.200
14/30 = 0.467
21/30 = 0.700
26/30 = 0.867
30/30 = 1.000
9
33 37 42 44 46 47 49 51 53 53 56 60 67 67 71 79
Cumulative
Percentage
20.0
46.7
70.0
86.7
100.0
33
Chapter 2
34

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