Question

The following table shows the age distribution of patients of malaria in a village during a particular month:
$\begin{array}{ccccccc}\text{Age (in years)}& 5-14& 15-24& 25-34& 35-44& 45-54& 55-64\\ \text{Number of cases}& 6& 11& 21& 23& 14& 5\end{array}$

Answer 1

Converting the series into exclusive form, we get:

Class	Frequency($f_i$)	Mid values ($x_i$)	$u_i=\frac{x_i-A}{h}$ $u_i=\frac{x_i-29.5}{10}$	$\left(f_i{u}_i\right)$
5 - 14	6	9.5	-2	-12
15 - 24	11	19.5	-1	-11
25 - 34	21	29.5 = A	0	0
35 - 44	23	39.5	1	23
45 - 54	14	49.5	2	28
55 - 64	5	59.5	3	15
Total	∑($f_i$)=80			∑$\left(f_i{u}_i\right)$ = 43

Now,
A = 29.5, h = 10, ∑($f_i$) = 80, ∑$\left(f_i{u}_i\right)$ = 43

Therefore,
Mean = A + $h\times \frac{\sum f_i{u}_i}{\sum f_i}$

= 29.5 + $10\times \frac{43}{80}$

= 29.5 + 5.375

= 34.875

Therefore, $\overline{x}$= 34.875.

Therefore, The average age of the patients is 34.87 years