Question

The following table shows the age distribution of cases of a certain disease admitted during a year in a particular hospital

Age (in Years)	5 - 14	15 - 24	25 - 34	35 - 44	45 - 54	55 - 64
No. of Cases	6	11	21	23	14	5

Find the nearest integer to the modal age.

Answer 1

Here class intervals are not in inclusive form. So, first convert the above frequency table in inclusive form and it is given by

Age(in years)	$4.5-14.5$	$14.5-24.5$	$24.5-34.5$	$34.5-44.5$	$44.5-54.5$	$54.5-64.5$
No. of classes	$6$	$11$	$21$	$23$	$14$	$5$

Class $34.5-44.5$, has maximum frequency.

$⟹34.5-44.5$ is the modal calss
$\therefore l=34.5,h=10,f_o=21,f_1=23and{f}_2=14$
Mode $=l+\frac{f_1-f_o}{2f_1-f_o-f_2}\times h$

$⟹$ Mode $=34.5+\frac{23-21}{46-21-14}\times 10=34.5+\frac{2}{11}\times 10=36.31$

Hence, the answer is $36$.