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Question
The mean of the following distribution is `21 1/7`. Find the value of ‘f’.
| C.I. | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency | 8 | 22 | 31 | f | 2 |
Solution
`barx = 21 1/7 = 148/7`
| C.I. | Frequency | Mid-value (xi) | fixi |
| 0 – 10 | 8 | 5 | 40 |
| 10 – 20 | 22 | 15 | 330 |
| 20 – 30 | 31 | 25 | 775 |
| 30 – 40 | f | 35 | 35f |
| 40 – 50 | 2 | 45 | 90 |
| Total | 63 + f | 1235 + 35f |
`barx = (sumf_ix_i)/(sumf_i) = (1235 + 35f)/(63 + f)`
`=> 148/7 = (1235 + 35f)/(63 + f)`
`=> 9324 + 148f = 8645 + 245f`
`=> 245f - 148f = 9324 - 8645`
`=> f = 679/97 `
`=>` f = 7
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