Question

An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health insurance policies are given to persons of age 15 years and onwards, but less than 60 years.

Age (in yrs)	Number of policy holders
15 – 20	2
20 – 25	4
25 – 30	18
30 – 35	21
35 – 40	33
40 – 45	11
45 – 50	3
50 – 55	6
55 – 60	2

Find the modal age and median age of the policy holders.

Answer 1

Modal Age:

Maximum frequency is 33, which lies in the class 35 – 40.

Modal class = 35 – 40

l = 35, f₁ ​= 33, f₀ ​= 21, f₂ ​= 11, h = 5

Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

Mode = `35 + ((33 - 21)/(2(33) - 21 - 11)) xx 5`

Mode = `35 + (12/(66 - 32)) xx 5`

Mode = `35 + 60/34`

= 35 + 1.76

= 36.76

Median Age:

Age	Frequency (f)	Cumulative Frequency (cf)
15 – 20	2	2
20 – 25	4	6
25 – 30	18	24
30 – 35	21	45
35 – 40	33	78
40 – 45	11	89
45 – 50	3	92
50 – 55	6	98
55 – 60	2	100

N = 100 ⇒ `N/2` = 50

Median class is 35 – 40 (since cf just greater than 50 is 78).

l = 35, cf = 45, f = 33, h = 5

Median = `l + ((N/2 - cf)/f) xx h`

Median = `35 + ((50 - 45)/33) xx 5`

Median = `35 + 25/33`

= 35 + 0.76

= 35.76

Modal age is 36.76 years and Median age is 35.76 years.