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Question
If the mean of the following distribution is 24, find the value of 'a '.
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Number of students |
7 | a | 8 | 10 | 5 |
Solution
We have,
| C.I. | f |
Class mark x |
fx |
| 0 - 10 | 7 | 5 | 35 |
| 10 - 20 | a | 15 | 15a |
| 20 - 30 | 8 | 25 | 200 |
| 30 - 40 | 10 | 35 | 350 |
| 40 - 50 | 5 | 45 | 225 |
| `sumf = 30 + a` | `sumfx = 810 + 15a` |
Mean 24 (given)
`=> (sumfx)/(sumf) = 24 => (810+15a)/(30 + a) = 24 => 810 + 15a = 720 + 24a`
`=> a= 10`
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