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Question
The mean of the following distribution is 6. Find the value at P:
| x | 2 | 4 | 6 | 10 | P + 5 |
| f | 3 | 2 | 3 | 1 | 2 |
Solution
Calculation of Arithmetic Mean:
| `x_i` | `f_i` | `f_ix_i` |
| 2 | 3 | 6 |
| 4 | 2 | 8 |
| 6 | 3 | 18 |
| 10 | 1 | 10 |
| P + 5 | 2 | 2P + 10 |
| `sumf_i` = 11 | `sumf_ix_i` = 2P + 52 |
We have,
`sumf_i` = 11
`sumf_ix_i` = 2P + 52
∴ Mean = `(sumf_ix_i)/(sumf_i)`
6 = `(2P + 52)/(11)`
⇒ 66 = 2P + 52
⇒ 2P = 66 - 52
⇒ 2P = 14
⇒ P = 7.
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