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Question
Find the missing value of p for the following distribution whose mean is 12.58.
| x | 5 | 8 | 10 | 12 | p | 20 | 25 |
| f | 2 | 5 | 8 | 22 | 7 | 4 | 2 |
Solution
| x | f | fx |
| 5 | 2 | 10 |
| 8 | 5 | 40 |
| 10 | 8 | 80 |
| 12 | 22 | 264 |
| p | 7 | 7p |
| 20 | 4 | 80 |
| 25 | 2 | 50 |
| N = 50 | `sumfx = 7p + 524` |
Given mean = 12. 58
⇒ `(sumfx)/N = 12 . 58`
⇒ `(7p + 524)/50 = 12.58`
⇒ 7p + 524 = 629
⇒ 7p = 629 - 524
⇒ 7p = 105
⇒ `p = 105/7 = 15`
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