Question

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

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

Find the average age for which maximum cases occured.

Answer 1

Here class intervals are not inclusive form. So, we first convert them in inclusive from by subtracting $h/2$ from the lower limit and adding $h/2$ to the upper limit of each class, where h is the difference between the lower limit of a class and the upper limit of the preceding class. The given frequency distribution in inclusive form is as follows.

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 cases:	6	11	21	23	14	5

We observe that the class $34.5-44.5$ has the maximum frequency. So, it is the modal class such that,
$l=34.5,h=10,f=23,f_1=21,and{f}_2=14$
$\therefore Mode=l+\frac{f-f_1}{2f-f_1-f_2}\times h$
$\Rightarrow Mode=34.5+\frac{23-21}{46-21-14}\times 10$
$\Rightarrow Mode=34.5+\frac{1}{11}\times 10$
$\Rightarrow Mode=36.31$