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Question
If the mean of the following distribution is 7.5, find the missing frequency ‘f’:
| Variable : | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Frequency: | 20 | 17 | f | 10 | 8 | 6 | 7 | 6 |
Solution
| Variable | Frequency `(f)` | `fx` |
| 5 | 20 | 100 |
| 6 | 17 | 102 |
| 7 | f | 7f |
| 8 | 10 | 80 |
| 9 | 8 | 72 |
| 10 | 6 | 60 |
| 11 | 7 | 77 |
| 12 | 6 | 72 |
| `sumf` = 74 + `f` | 563 + 7`f` |
∵ M = `(sumfx)/(sumf)`
∴ 7.5 = `(563 + 7f)/(74 + f)`
∴ 555 + 7.5f = 563 + 7f
∴ 0.5f = 8
∴ f = 16.
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