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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 | `sum`fx = 7P + 524 |
Given
⇒ Mean = 12.58
`rArr(sumfx)/N=12.58`
`rArr(7P+524)/50=12.58`
⇒ 7P + 524 = 12.58(50)
⇒ 7P + 524 = 629
⇒ 7P = 629 - 524
⇒ 7P = 105
`rArrP=105/7`
P = 15
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