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Question
Find the value of p for the following distribution whose mean is 16.6
| x | 8 | 12 | 15 | P | 20 | 25 | 30 |
| f | 12 | 16 | 20 | 24 | 16 | 8 | 4 |
Solution
| x | f | fx |
| 8 | 12 | 96 |
| 12 | 16 | 192 |
| 15 | 20 | 300 |
| P | 24 | 24P |
| 20 | 16 | 220 |
| 25 | 8 | 200 |
| 30 | 4 | 420 |
| N = 100 | `sum` fx = 24P + 1228 |
Given
⇒ Mean = 16.6
`rArr(sumfx)/N=16.6`
`rArr(24P+1228)/100`
⇒ 24P + 1228 = 1660
⇒ 24P = 1660 - 1228
`rArrP=432/24`
⇒ P = 18
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