Find the mean of the following data, using step - deviation method:
Class | 5 - 15 | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 |
Frequency | 6 | 10 | 16 | 15 | 24 | 8 | 7 |
We will find the mean of the data using step - deviation method, where A = Assumed mean and h = length of class interval.
Here, let A = 40 and h = 10
CLASS | MID - POINT(xi) | DEVIATION(di) di = xi – 40 | FREQUENCY(fi) | ui = di/h | fiui |
5 - 15 | 10 | - 30 | 6 | - 3 | - 18 |
15 - 25 | 20 | - 20 | 10 | - 2 | - 20 |
25 - 35 | 30 | - 10 | 16 | - 1 | - 16 |
35 - 45 | 40 = A | 0 | 15 | 0 | 0 |
45 - 55 | 50 | 10 | 24 | 1 | 24 |
55 - 65 | 60 | 20 | 8 | 2 | 16 |
65 - 75 | 70 | 30 | 7 | 3 | 21 |
TOTAL | 86 | 7 |
We have got
A = 40, h = 10, Σfi = 86 & Σfiui = 7
∵ mean is given by
⇒ 
⇒ 
Thus, mean is 40.81
20