Frequency Distribution
Statistical data
obtained by means of census, sample surveys or experiments usually consist of
raw, unorganized sets of numerical values.
Before these data can be used as a basis for inferences about the
phenomenon under investigation or as a basis for decision, they must be
summarized and the pertinent information must be extracted.
Example 1
A random sample of
100 households in a town was selected and their monthly town gas consumption
(in cubic metres) in last month were recorded as follows:
|
55
|
82
|
83
|
109
|
78
|
87
|
95
|
94
|
85
|
67
|
|
80
|
109
|
83
|
89
|
91
|
104
|
90
|
103
|
67
|
52
|
|
107
|
78
|
86
|
29
|
72
|
66
|
92
|
99
|
60
|
75
|
|
88
|
112
|
97
|
88
|
49
|
62
|
70
|
66
|
88
|
62
|
|
72
|
85
|
81
|
78
|
77
|
41
|
105
|
92
|
94
|
74
|
|
78
|
75
|
87
|
83
|
71
|
99
|
56
|
69
|
78
|
60
|
|
1197
|
39
|
104
|
86
|
67
|
79
|
98
|
102
|
82
|
91
|
|
46
|
120
|
73
|
125
|
132
|
86
|
48
|
55
|
112
|
28
|
|
42
|
24
|
130
|
100
|
46
|
57
|
31
|
129
|
137
|
59
|
|
102
|
51
|
135
|
53
|
105
|
110
|
107
|
46
|
108
|
117
|
A useful method for
summarizing a set of data is the construction of a frequency table, or a
frequency distribution. That is, we
divide the overall range of values into a number of classes and count the
number of observations that fall into each of these classes or intervals.
The general rules
for constructing a frequency distribution are:
(i)
There
should not be too few or too many classes.
(ii) Insofar
as possible, equal class intervals are preferred. But the first and last classes can be
open-ended to cater for extreme values.
In example 1, the
sample size is 100 and the range for the data is 113 (137 - 24). A frequency
distribution with six classes is appropriate and it is shown below.
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