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Question
The arithmetic mean of the following data is 25, find the value of k.
| x1 | 5 | 15 | 25 | 35 | 45 |
| f1 | 3 | k | 3 | 6 | 2 |
Solution
| x | f | fx |
| 5 | 3 | 15 |
| 15 | k | 15k |
| 25 | 3 | 75 |
| 35 | 6 | 210 |
| 45 | 2 | 90 |
| N = k + 14 | `sum`fx = 15k + 390 |
Given
Mean = 25
`rArr(sumfx)/N=25`
`rArr(15k+390)/(k+14)=25`
⇒ 15k + 390 = 25(k + 14)
⇒ 15k + 390 = 25k + 350
⇒ 25k - 15k = 390 - 350
⇒ 10k = 40
`rArr k=40/10`
⇒ k = 4
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