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प्रश्न
Find the mean of the following frequency distribution using step-deviation method
| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency | 7 | 10 | 15 | 8 | 10 |
उत्तर
Let us choose a = 25, h = 10, then `d_i = x_i – 25 and u_i = (x_i−25)/10`
Using step-deviation method, the given data is shown as follows:
| Class | Frequency `(f_i)` | Class mark `(x_i)` | `d_i = x_i `– 25 | `u_i =( x_i−25)/10` | `(f_i u_i)` |
| 0 –10 | 7 | 5 | -20 | -2 | -14 |
| 10 – 20 | 10 | 15 | -10 | -1 | -10 |
| 20 – 30 | 15 | 25 | 0 | 0 | 0 |
| 30 – 40 | 8 | 35 | 10 | 1 | 8 |
| 40 – 50 | 10 | 45 | 20 | 2 | 20 |
| Total | `Ʃ f_i` = 50 | `Ʃ f_i u_i = 4` |
The mean of the data is given by,
x = a + `((sum _i f_i u_i)/(sum _i f_i)) xx h`
=`25+ 4/50 xx 10`
=`25+ 4/5`
=`(125+4)/5`
= `129/5`
= 25.8
Thus, the mean is 25.8.
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