Question

The following 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

Answer 1

Here class intervals are not in inclusive form So Converting the above frequency table in inclusive form

Age (in year)	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 Cases	6	11	21	23	14	5

Class 34.5 - 44.5 has maximum frequency So it is the modal class
$\iota =34.5,h=10,f_0=21,f_1=23and{f}_2=14$

$\therefore Mode=\iota +\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

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

= 34.5 + $\frac{2}{11}$ x 10 = 36.31