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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 | `sum`fx = 9P + 303 |
Given
⇒ Mean = 7.68
`rArr(sumfx)/N=7.68`
`rArr(9P+303)/(P+41)=7.68`
⇒ 9P + 303 = 7.68(P + 41)
⇒ 9P + 303 = 7.68P + 314.88
⇒ 9P - 7.68P = 314.88 - 303
⇒ 1.32P = 11.88
`rArrP=11.88/1.32`
⇒ P = 9
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