Find the arithmetic mean of the following frequency distribution using step - deviation method:
Age (in years) | 18 - 24 | 24 - 30 | 30 - 36 | 36 - 42 | 42 - 48 | 48 - 54 |
Number of workers | 6 | 8 | 12 | 8 | 4 | 2 |
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 = 33 and h = 6
AGE(years) | MID - POINT(xi) | DEVIATION(di) di = xi – 33 | NUMBER OF WORKERS(fi) | ui = di/h | fiui |
18 - 24 | 21 | - 12 | 6 | - 2 | - 12 |
24 - 30 | 27 | - 6 | 8 | - 1 | - 8 |
30 - 36 | 33 = A | 0 | 12 | 0 | 0 |
36 - 42 | 39 | 6 | 8 | 1 | 8 |
42 - 48 | 45 | 12 | 4 | 2 | 8 |
48 - 54 | 51 | 18 | 2 | 3 | 6 |
TOTAL | 40 | 2 |
We have got
A = 33, h = 6, Σfi = 40 & Σfiui = 2
∵ mean is given by
⇒
⇒
Thus, mean age is 33.3 years.