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Question
Find the mean of the following frequency distribution by the step deviation method :
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | 120-140 |
| Frequency | 12 | 24 | 52 | 88 | 66 | 42 | 16 |
Solution
| Class Interval | xi | fi | A = 70 `"u" = ("x - A")/"h"_i` |
`f_iu` |
| 0-20 | 10 | 12 | -3 | -36 |
| 20-40 | 30 | 24 | -2 | -48 |
| 40-60 | 50 | 52 | -1 | -52 |
| 60-80 | A = 70 | 88 | 0 | 0 |
| 80-100 | 90 | 66 | 1 | 66 |
| 100-120 | 110 | 42 | 2 | 84 |
| 120-140 | 130 | 16 | 3 | 48 |
| Total | 300 | 62 |
A= 70 and hi = 20
`barx = "A" + "h" xx (Σf_i "u")/(Σf_i)`
`barx = 70 + 20 xx 62/300`
`barx = 70 + 4.13`
`barx = 74.13`
∴ Mean = 74.13
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