HOSP 1207 (Business Stats)
Learning Centre
Frequency Distributions
Frequency tables are used to organize a large set of quantitative data into something
easier to understand. Frequency tables can be constructed to show individual data
values (x) and the number of times each value occurs or frequency, f(x). This is an
ungrouped frequency distribution. Frequency tables can also be constructed by
breaking data into smaller classes (intervals) and showing how many data values are in
each class. This is called a grouped frequency distribution.
Example: Set up a grouped frequency distribution for the data shown below.
15
42
9
4
16
21
18
39
5
10
26
20
15
14
2
18
17
6
11
45
3
19
5
15
22
24
35
40
41
33
25
21
11
13
2
3
1
12
30
32
1. Determine the number of classes and class width. If you are told to create a table
with 7 classes, use the formula (largest data value – smallest data value)/desired
number of classes and round up your answer. If you are not told how many
classes to create, use this formula for class width:
Class width
largest data value
smallest data value
(number of data values)
45
1
√40
6.96 ≈ 7
Always round up to the next whole number for class width.
2. Construct the classes for your table. The lower class limit is the lowest data
value counted in that class. Find the smallest data value in the set; this will be the
lower limit of the first class. For the data above, the lower class limit of the first
class is 1. To find the next lower class limit, add the class width (ex. 1 + 7 = 8,
the second lower class limit). Continue for all the following classes.
3. Then fill in the upper class limits which will be the same as the lower class limit of
the next class. Note that for the class 1–8, this includes all values UP TO 8 (e.g.
7.7) EXCEPT for 8 itself. So the data value 8, would not be counted in the class:
1–8, but in the class 8–15.
4. Count how many data values occur within the created class intervals and enter
this information into the “frequency” column.
5. To find the midpoint of a class in a grouped frequency distribution, take the
average of the upper and lower limits of a class.
6. To find the relative frequency of a particular class, divide the class frequency f
by the total of all the frequencies (which equals the sample size, n).
See next page for completed frequency table
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes.
Authored by
by Emily
EmilySimpson
Simpson
Class Limits (lower to upper)
1–8
8–15
15–22
22–29
29–36
36–43
43–50
Frequency
7
11
9
5
4
4
1
Midpoint
4.5
10.5
18.5
25.5
32.5
39.5
46.5
Relative Frequency
7/ 41 = 0.17
0.27
0.22
0.12
0.10
0.10
0.02
Exercises.
1. Construct an ungrouped frequency distribution table for the following data set:
{1, 2, 3, 4, 6, 2, 2, 4, 5, 9, 8, 1, 3, 2, 3, 8}
2. Construct a grouped frequency distribution table for the data below. Find the
midpoint and relative frequency for each class. Is the distribution bimodal? Is the
distribution skewed?
55
32
44
60
90
45
42
62
85
38
77
41
87
77
91
50
80
53
72
74
45
36
76
75
87
80
46
52
38
33
83
39
37
71
82
79
51
87
25
91
34
87
38
26
39
90
88
22
33
82
x
1
2
3
4
5
6
7
3. From the ungrouped frequency distribution table shown to the
right, write out the corresponding data set.
ANSWERS
1.
f(x)
3
5
6
4
3
2
1
2. Class width = 10
x
1
2
3
4
5
6
7
8
9
Class
Limits
22-32
f(x)
2
4
3
2
1
1
0
2
1
3. {1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3,
3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7}
Frequency
Midpoint
3
27
Relative
Frequency
0.06
32-42
12
37
0.24
42-52
7
47
0.14
52-62
4
57
0.08
62-72
2
67
0.04
72-82
9
77
0.18
82-92
13
87
0.26
The distribution is bimodal; not
skewed.
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes.
2