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Question
The following table gives the frequency distribution of married women by age at marriage:
| Age (in years) | Frequency |
| 15-19 | 53 |
| 20-24 | 140 |
| 25-29 | 98 |
| 30-34 | 32 |
| 35-39 | 12 |
| 40-44 | 9 |
| 45-49 | 5 |
| 50-54 | 3 |
| 55-59 | 3 |
| 60 and above | 2 |
Calculate the median and interpret the results.
Solution
| Class interval (exclusive) |
Class interval (inclusive) |
Frequency | Cumulative frequency |
| 15-19 | 14.5 - 19.5 | 53 | 53 |
| 20-24 | 19.5 - 24.5 | 140 | 193 |
| 25-29 | 24.5 - 29.5 | 98 | 291 |
| 30-34 | 29.5 - 34.5 | 32 | 323 |
| 35-39 | 34.5 - 39.5 | 12 | 335 |
| 40-44 | 39.5 - 44.5 | 9 | 344 |
| 45-49 | 44.5 - 49.5 | 5 | 349 |
| 50-54 | 49.5 - 54.5 | 3 | 352 |
| 54-59 | 54.5 - 59.5 | 3 | 355 |
| 60 and above | 59.5 and above | 2 | 357 |
| N = 357 |
N = 357
`N/2=357/2=178.5`
The cumulative frequency just greater than N/2 is 193, then the median class is 19.5-24.5
Such that
l = 19.5, f = 140. F = 53, h = 24.5 - 19.5 = 5
Median `=l+(N/2-F)/fxxh`
`=19.5+(178.5 - 53)/140xx5`
`=19.5+125.5/140xx5`
`=19.5+627.5/140`
= 19.5 + 4.48
= 23.98
Nearly half the a women were married between ages 15 and 25.
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