The following table gives the frequency distribution of married women by age at marriage:

Age (in years)	Frequency	Age (in years)	Frequency
15-19	53	40-44	9
20-24	140	45-49	5
25-29	98	50-54	3
30-34	32	55-59	3
35-39	12	60 and above	2

Calculate the median and interpret the results.

Given:

The given table gives the frequency distribution of married women by age at marriage.

To do:

We have to find the median and interpret the results.

Solution:

Arranging the classes in exclusive form and then forming its cumulative frequency table as below, we get,

Here,

$N = 357$

$\frac{N}{2} = \frac{357}{2} = 178.5$

The cumulative frequency just greater than $\frac{N}{2}$ is 193 and the corresponding class is 20 – 24. 

This implies, 19.5 – 24.5 is the median class.

Therefore,

$l = 19.5, f = 140, F = 53$ and $h = (24.5 - 19.5) = 5$

Medain $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$

$=19.5+\frac{178.5-53}{140} \times 5$

$=19.5+\frac{125.5}{140} \times 5$

$=19.5+\frac{125.5}{28}$

$= 19.5 + 4.48$

$= 23.98$

This implies, nearly half the women were married between the ages of 15 and 24 years.

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Updated on: 10-Oct-2022

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