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Question

The following table gives the frequency distribution of married women by age at marriage:
Age
(in years)
Frequency Age
(in years)
Frequency
15−19
20−24
25−29
30−34
35−39
53
140
98
32
12
40−44
45−49
50−54
55−59
60 and above
9
5
3
3
2

Calculate the median and interpret the results.

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Solution

Here, the frequency table is given in inclusive form. So, we first transform it into exclusive form by subtracting and adding h/2 to the lower and upper limits respectively of each class, where h denotes the difference of lower limit of a class and upper limit of the previous class.

We have, N = 357
So, N/2 = 178.5

Thus, the cumulative frequency just greater than 178.5 is 193 and the corresponding class is 19.5−24.5.

Therefore, 19.5−24.5 is the median class.

Here, l = 19.5, f = 140, F = 193 and h = 5

We know that

=19.5+178.5-53140×5=19.5+125.5140×5=19.5+125.528=546+125.528=23.98

Hence, the median age 23.98 years.

Thus, nearly half the women were married between the age of 19.5 years and 24.5 years.


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