Probability Distributions Worksheets Page 3
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8A37
A P P E N D I X C . 5
Probability Distributions
Example 3
Constructing a Grouped Frequency Distribution
A city has 48 general practice physicians who treated the following numbers
of patients during a two-week period in January of 2008. Construct a grouped
frequency distribution and histogram for these data.
107
162
184
170
177
102
145
141
105
193
167
149
195
127
193
191
150
153
164
167
171
163
141
129
109
171
150
138
100
174
147
153
171
163
118
142
107
144
100
132
153
107
124
162
192
134
187
177
To begin constructing a grouped frequency distribution, you must
SOLUTION
first decide on the number of groups. There are several ways to group these data.
However, the smallest number is 100 and the largest is 195, so 10 groups of 10
each are appropriate. The first group is 100–109, the second group is 110–119,
and so on. By tallying the data in the 10 groups, you can obtain the following
grouped frequency distribution.
Group
Event
n x
100–109
100, 100, 102, 105, 107, 107, 107, 109
8
110–119
118
1
120–129
124, 127, 129
3
130–139
132, 134, 138
3
140–149
141, 141, 142, 144, 145, 147, 149
7
150–159
150, 150, 153, 153, 153
5
160–169
162, 162, 163, 163, 164, 167, 167
7
170–179
170, 171, 171, 171, 174, 177, 177
7
180–189
184, 187
2
190–199
191, 192, 193, 193, 195
5
Total 48
A histogram for this grouped frequency distribution is shown in Figure C.20.
✓
CHECKPOINT 3
Grouped Frequency Distribution
The numbers of minutes 25
n(x)
Internet subscribers spent on
8
the Internet in the past week are
7
6
listed below. Construct a grouped
5
frequency distribution and
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histogram for these data.
3
2
1
45
27
6
60
38
x
63
61
34
37
43
100 110 120 130 140 150 160 170 180 190 200
33
38
21
71
81
Patients treated
30
45
33
64
52
■
68
35
32
54
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