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Question
Find the mean of the following frequency distribution by the step deviation method :
| Class | 100-110 | 110-120 | 120-130 | 130-140 | 140-150 |
| Frequency | 15 | 18 | 32 | 25 | 10 |
Solution
| Class Interval | xi | fi | A = 125 `"u" = ("x - A")/"h"_"i"` |
fiu |
| 100-110 | 105 | 15 | -2 | -30 |
| 110-120 | 115 | 18 | -1 | -18 |
| 120-130 | A = 125 | 32 | 0 | 0 |
| 130-140 | 135 | 25 | 1 | 25 |
| 140-150 | 145 | 10 | 2 | 20 |
| Total | 100 | -3 |
A=125 and hi = 10
`barx = A + "h" xx (Σf_i "u")/(Σf_i)`
`barx = 125 + 10 xx (-3)/100`
`barx = 125-0.3`
`barx = 124.70`
∴ Mean = 124.70
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