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Question
Find the mean of the following data, using step-deviation method:
| Class | 5 – 15 | 15-20 | 20-35 | 35-45 | 45-55 | 55-65 | 65-75 |
| Frequency | 6 | 10 | 16 | 15 | 24 | 8 | 7 |
Solution
Let us choose a = 40, h = 10, then `d_i = x_i – 40 and u_i =(x_i-40)/10`
Using step-deviation method, the given data is shown as follows:
| Class | Frequency `(f_i)` | Class mark `(x_i)` | `d_i = x_i` – 40 | `u_i = (x_i−40)/10` | `(f_i u _i)` |
| 5 – 15 | 6 | 10 | -30 | -3 | -18 |
| 15 – 25 | 10 | 20 | -20 | -2 | -20 |
| 25 – 35 | 16 | 30 | -10 | -1 | -16 |
| 35 – 45 | 15 | 40 | 0 | 0 | 0 |
| 45 – 55 | 24 | 50 | 10 | 1 | 24 |
| 55 – 65 | 8 | 60 | 20 | 2 | 16 |
| 65 – 75 | 7 | 70 | 30 | 3 | 21 |
| Total | `Ʃ f_i` = 86 | `Ʃ f_i u_i `= 7 |
The mean of the data is given by,
x = a+ `((sum _i f_i u_i)/(sum _i f_i)) xx h`
= 40 + `7/86 xx 10`
=`40+ 70 / 86`
= 40 +0.81
= 40.81
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