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Question
Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
| Age in years | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| No. of persons | 5 | 25 | ? | 18 | 7 |
Solution
| Class interval | Frequency | Cumulative frequency |
| 0 - 10 | 5 | 5 |
| 10 - 20 | 25 | 30 |
| 20 - 30 | x | 30 + x |
| 30 - 40 | 18 | 48 + x |
| 40 - 50 | 7 | 55 + x |
| N = 55 + x |
Given
Median = 24
Then median class = 20 - 30
l = 20, h = 30 - 20 = 10, F = 30 and f = x
Median `=l+{(N/2-F)/f}xxh`
`24=20+((55+x)/2-30)/x xx10`
`24 - 20=((55+x)/2-30)/x xx10`
`4x=((55+x)/2-30)xx10`
`4x xx2=(55 + x -60)xx10`
8x = 550 + 10x - 600
10x - 8x = 600 - 550
2x = 50
x = 25
∴ Missing frequency = 25
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