Find the mean of the following data using step - deviation method:
Class | 500 - 520 | 520 - 540 | 540 - 560 | 560 - 580 | 580 - 600 | 600 - 620 |
Frequency | 14 | 9 | 5 | 4 | 3 | 5 |
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 = 550 and h = 20
CLASS | MID - POINT(xi) | DEVIATION(di) di = xi – 550 | FREQUENCY(fi) | ui = di/h | fiui |
500 - 520 | 510 | - 40 | 14 | - 2 | - 28 |
520 - 540 | 530 | - 20 | 9 | - 1 | - 9 |
540 - 560 | 550 = A | 0 | 5 | 0 | 0 |
560 - 580 | 570 | 20 | 4 | 1 | 4 |
580 - 600 | 590 | 40 | 3 | 2 | 6 |
600 - 620 | 610 | 60 | 5 | 3 | 15 |
TOTAL | 40 | - 12 |
We have got
A = 550, h = 20, Σfi = 40 & Σfiui = - 12
∵ mean is given by
⇒
⇒
Thus, mean is 544.