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प्रश्न
Find the mean by step deviation method.
| Class | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |
| Frequency | 5 | 6 | 8 | 12 | 6 | 3 |
योग
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उत्तर
1. Formula
The formula for finding the mean using the step-deviation method is:
Mean `(barx) = A + ((sumf_iu_i)/(sumf_i)) xx h`
Where:
A = Assumed mean (middle value from class marks xi)
h = Class width (upper limit – lower limit = 15 – 10 = 5)
`u_i = (x_i - A)/h`
xi = Class mark (midpoint of each class) = `("Lower limit" + "Upper limit")/2`
2. Calculation table
The assumed mean A = 22.5 and class width h = 5:
| Class | Frequency (fi) |
Class Mark (xi) |
`bb(u_i = (x_i - 22.5)/5)` | fiui |
| 10 – 15 | 5 | 12.5 | –2 | –10 |
| 15 – 20 | 6 | 17.5 | –1 | –6 |
| 20 – 25 | 8 | 22.5 (A) | 0 | 0 |
| 25 – 30 | 12 | 27.5 | 1 | 12 |
| 30 – 35 | 6 | 32.5 | 2 | 12 |
| 35 – 40 | 3 | 37.5 | 3 | 9 |
| Total | Σfi = 40 | Σfiui = 40 |
3. Substitute values into the formula
Substituting the sums into the step deviation equation:
`barx = 22.5 + (17/40) xx 5`
`barx = 22.5 + 17/8`
`barx` = 22.5 + 2.125
`barx` = 24.625
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