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Question
Find the mean of the following frequency distribution by the short cut method :
| Class | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 |
| Frequency | 7 | 10 | 14 | 17 | 15 | 11 | 6 |
Solution
| Class Interval | xi | fi | A = 35.5 d = x - A |
fid |
| 1-10 | 5.5 | 7 | -30 | -210 |
| 11-20 | 15.5 | 10 | 20 | -200 |
| 21-30 | 25.5 | 14 | -10 | -140 |
| 31-40 | A = 35.5 | 17 | 0 | 0 |
| 41-50 | 45.5 | 15 | 10 | 150 |
| 51-60 | 55.5 | 11 | 20 | 220 |
| 61-70 | 65.5 | 6 | 30 | 180 |
| Total | 80 | 0 |
`barx = A + (Σf_i d)/(Σf_i)`
`barx = 35.5 + 0/80`
`barx = 35.5 + 0`
`barx = 35.5`
∴ Mean = 35.5
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