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Question
The mean of the following distribution is 52 and the frequency of class interval 30-40 is ‘f’. Find ‘f’.
| Class Interval | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency | 5 | 3 | f | 7 | 2 | 6 | 13 |
Solution
The mean of the distribution is frequency
| C.I. | Frequency (f) |
Mid Value (x) |
fx |
| 10-20 | 5 | 15 | 75 |
| 20-30 | 3 | 25 | 75 |
| 30-40 | f | 35 | 35f |
| 40-50 | 7 | 45 | 315 |
| 50-60 | 2 | 55 | 110 |
| 60-70 | 6 | 65 | 390 |
| 70-80 | 13 | 75 | 975 |
| `sumf = 36 + f` | `sum fx = 1940 + 35 f` |
Mean = `(sumfx)/(sumf)`
`=> 52 = (1940 + 35f)/(36 + f)`
`=>` 1872 + 52f = 1940 + 35f
`=>` 17f = 68
∴ f = 4
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