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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 |
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.