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 |
We will find the mean of the frequency distribution using step - deviation method, where A = Assumed mean and h = length of class interval.
Here, let A = 25 and h = 10
CLASS | MID - POINT(xi) | DEVIATION(di) di = xi – 25 | FREQUENCY(fi) | ui = di/h | fiui |
0 - 10 | 5 | - 20 | 7 | - 2 | - 14 |
10 - 20 | 15 | - 10 | 10 | - 1 | - 10 |
20 - 30 | 25 = A | 0 | 15 | 0 | 0 |
30 - 40 | 35 | 10 | 8 | 1 | 8 |
40 - 50 | 45 | 20 | 10 | 2 | 20 |
TOTAL | 50 | 4 |
We have got
A = 25, h = 10, Σfi = 50 & Σfiui = 4
∵ mean is given by
⇒
⇒
Thus, mean is 25.8