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Question
Find the value of p, if the mean of the following distribution is 20.
| x | 15 | 17 | 19 | 20+P | 23 |
| f | 2 | 3 | 4 | 5P | 6 |
Solution
| x | f | fx |
| 15 | 2 | 30 |
| 17 | 3 | 51 |
| 19 | 4 | 76 |
| 20+P | 5P | 100P + 5P2 |
| 23 | 6 | 138 |
| N = 5P + 15 | `sum`fx = 295 + 100P + 5P2 |
Given
⇒ Mean = 20
`rArr(sumfx)/N=20`
`rArr(295+100P+5P^2)/(5P+15)=20`
⇒ 295 + 100P + 5P2 = 20(5P + 15)
⇒ 295 + 100P + 5P2 = 100P + 300
⇒ 100P - 100P + 5P2 = 300 - 295
⇒ 5P2 = 5
⇒ P2 = 1
⇒ P = 1
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