Question

The following data shows that the age distribution of patients of malaria in a village during a particular month. Find the average age of the patients.

Age (in years)	No. of cases
5-14	6
15-24	11
25-34	21
35-44	23
45-54	14
55-64	5
65-74	3

• A. $36.12$ years
• B. $36.13$ years
• C. $13.36$ years
• D. $23.36$ years

Answer 1

The correct option is B $36.13$ years

Age (in years)	No. of Cases (Fi)	Mid Point (Xi)	$FiXi$
5-14	6	9.5	57
15-24	11	19.5	214.5
25-34	21	29.5	619.5
35-44	23	39.5	908.5
45-54	14	49.5	693
55-64	5	59.5	2975.
65-74	3	69.54	208.5
	$SigmaFi=83$		$\Sigma FiXi=2998.5$

For grouped data when class interval is given, we find the class mark.

Class mark $=$ midpoint of an interval $=\frac{(Lowerlimit+Upperlimit)}{2}$

Class mark is taken as $x_i$ for each class interval, find $x_i{f}_i$.

Now mean age $=\frac{\Sigma x_i{f}_i}{\Sigma f_i}=\frac{2998.5}{83}=36.1265=36.13$