Calculate the mean of the following distribution using step deviation method.
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Number of students |
10 | 9 | 25 | 0 | 16 | 10 |
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Solution
Let the assumed mean A = 25
| Marks |
Mid-value x |
f | d = x - A | `t= (x-A)/i = (x-25)/10` | ft |
| 0 - 10 | 5 | 10 | -20 | -2 | -20 |
| 10 - 20 | 15 | 9 | -10 | -1 | -9 |
| 20 - 30 | 25 | 25 | 0 | 0 | 0 |
| 30 - 40 | 35 | 30 | 10 | 1 | 30 |
| 40 - 50 | 45 | 16 | 20 | 2 | 32 |
| 50 - 60 | 55 | 10 | 30 | 3 | 30 |
| `sumf= 100` | `sumft = 63` |
`:. Mean = A+ (sumft)/(sumf) xx i = 25 + 63/100 xx 10 = 25 + 63/10 = 25 + 6.3 = 31.3`
Concept: Concept of Median
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