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Question
An incomplete distribution is given as follows:
| Variable: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |
| Frequency: | 10 | 20 | ? | 40 | ? | 25 | 15 |
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.
Solution
| Class interval | Frequency | Cumulative frequency |
| 0 - 10 | 10 | 10 |
| 10 - 20 | 20 | 30 |
| 20 - 30 | f1 | 30 + f1 |
| 30 - 40 | 40 | 70 + f1 |
| 40 - 50 | f2 | 70 + f1 + f2 |
| 50 - 60 | 25 | 95 + f1 + f2 |
| 60 - 70 | 15 | 110 + f1 + f2 |
| N = 170 |
Given median = 35
The median class = 30 - 40
l = 30, h = 40 - 30 = 10, f = 40, F = 30 + f1
Median `=l+{(N/2-F)/f}xxh`
`35=30+{(85-(30 + f1))/40}xx10`
`35=30+(55-f1)/40xx10`
`35-30=(55-f1)/4`
`5=(55-f1)/4`
5 x 4 = 55 - f1
20 = 55 - f1
f1 = 55 - 20
f1 = 35
Given
Sum of frequencies = 170
⇒ 10 + 20 + f1 + 40 + f2 + 25+ 15 = 170
⇒ 10 + 20 + 35 + 40 + f2 + 25+ 15 = 170
⇒ 145 + f2 = 170
⇒ f2 = 170 - 145
⇒ f2 = 25
∴ f1 = 35 and f2 = 25
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