The following table shows the age distribution of patients of malaria in a village during a particular month:
Age (in years) | 5 - 14 | 15 - 24 | 25 - 34 | 35 - 44 | 45 - 54 | 55 - 64 |
Number of cases | 6 | 11 | 21 | 23 | 14 | 5 |
Find the average age of the patients.
We will find the average age using step - deviation method, where A = Assumed mean and h = length of class interval.
Here, let A = 29.5 and h = 10
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 – 29.5 | NUMBER OF CASES(fi) | ui = di/h | fiui |
4.5 - 14.5 | 9.5 | - 20 | 6 | - 2 | - 12 |
14.5 - 24.5 | 19.5 | - 10 | 11 | - 1 | - 11 |
24.5 - 34.5 | 29.5 = A | 0 | 21 | 0 | 0 |
34.5 - 44.5 | 39.5 | 10 | 23 | 1 | 23 |
44.5 - 54.5 | 49.5 | 20 | 14 | 2 | 28 |
54.5 - 64.5 | 59.5 | 30 | 5 | 3 | 15 |
TOTAL | 80 | 43 |
We have got
A = 29.5, h = 10, Σfi = 80 & Σfiui = 43
∵ mean is given by
⇒ 
⇒ 
Thus, mean age is 34.88 years.