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Question
Find the missing frequency (p) for the following distribution whose mean is 7.68.
| x | 3 | 5 | 7 | 9 | 11 | 13 |
| f | 6 | 8 | 15 | p | 8 | 4 |
Solution
| x | f | fx |
| 3 | 6 | 18 |
| 5 | 8 | 40 |
| 7 | 15 | 105 |
| 9 | p | 9p |
| 11 | 8 | 88 |
| 13 | 4 | 52 |
| N = P + 41 | `sumfx = 9P + 303` |
Given mean = 7. 68
⇒`(sumfx)/N`= 7.68
⇒ `(9p + 303)/(p +41) = 7.68`
⇒ 9p + 303 = 7.68p + 314.88
⇒ 9p - 7.68 = 314.88 - 303
⇒ 1. 32p = 11.88
⇒ `p = (11.88)/1.32`
⇒ p = 9
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