Find the mean age from the following frequency distribution:
Age (in years) | 25 - 29 | 30 - 34 | 35 - 39 | 40 - 44 | 45 - 49 | 50 - 54 | 55 - 59 |
Number of persons | 4 | 14 | 22 | 16 | 6 | 5 | 3 |
We will find the mean age using step - deviation method, where A = Assumed mean and h = length of class interval.
Here, let A = 42 and h = 5
Since, the class intervals are inclusive type, we’ll first convert it into exclusive type by extending the class interval from both the ends.
AGE(years) | MID - POINT(xi) | DEVIATION(di) di = xi – 550 | NUMBER OF PERSONS(fi) | ui = di/h | fiui |
24.5 - 29.5 | 27 | - 15 | 4 | - 3 | - 12 |
29.5 - 34.5 | 32 | - 10 | 14 | - 2 | - 28 |
34.5 - 39.5 | 37 | - 5 | 22 | - 1 | - 22 |
39.5 - 44.5 | 42 = A | 0 | 16 | 0 | 0 |
44.5 - 49.5 | 47 | 5 | 6 | 1 | 6 |
49.5 - 54.5 | 52 | 10 | 5 | 2 | 10 |
54.5 - 59.5 | 57 | 15 | 3 | 3 | 9 |
TOTAL | 70 | - 37 |
We have got
A = 42, h = 5, Σfi = 70 & Σfiui = - 37
∵ mean is given by
⇒ 
⇒ 
Thus, mean age is 544 years.