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Question
The arithmetic mean of the following data is 14. Find the value of k
| x1 | 5 | 10 | 15 | 20 | 25 |
| f1 | 7 | k | 8 | 4 | 5 |
Solution
| x1 | f1 | x1f1 |
| 5 | 7 | 35 |
| 10 | k | 10k |
| 15 | 8 | 120 |
| 20 | 4 | 80 |
| 25 | 5 | 125 |
| `sumf_1=24+k` | `sumx_1f_1=360+10k` |
We know that mean, `barx=(sumx_1f_1)/(sumf_1)`
`14=(360+10k)/(24+k)`
By using cross multiplication method,
14(24 + k) = 360 + 10k
336 + 14k = 360 + 10k
14k - 10k = 360 - 336
4k = 24
`k=24/4`
Hence, k = 6
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