Question

The following table shows the age distribution of people suffering from asthma due to air pollution.

Age(in years)	7-11	11-15	15-19	19-23	23-27	27-31	31-35	35-39
No. of people	5	9	13	21	16	15	12	9

Find the mean age of persons suffering from asthma by using the direct method.

Answer 1

Age (in years) (Class interval)	Class Marks $\left(x_i\right)$	No. of people $\left(f_i\right)$	$\left(f_i\right)$$\left(x_i\right)$
7-11	9	5	45
11-15	13	9	117
15-19	17	13	221
19-23	21	21	441
23-27	25	16	400
27-31	29	15	435
31-35	33	12	396
35-39	37	9	333
Total	-	${\sum }_{}^{}{f}_i=100$	$\underset{}{\overset{}{\sum f_i{x}_i}}=2388$

$\mathrm{Mean}=\overline{x}=\frac{{\displaystyle \sum _{}^{}}{f}_i{x}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{2388}{100}=23.88\mathrm{years}$
Therefore, mean age of persons suffering from asthma is 23.88 years.