Question

The following frequency distribution table gives the ages of 200 patients treated in a hospital in a week. Find the mode of ages of the patients.

Age (years)	Less than 5	5 - 9	10 - 14	15 - 19	20 - 24	25 - 29
No. of patients	38	32	50	36	24	20

Answer 1

Class Age (years)	Continuous class	Frequency  (No. of patients)
Less than 5	0 − 4.5	38
5 − 9	4.5 − 9.5	32 → f0
10 − 14	9.5 − 14.5	50 → f1
15 − 19	14.5 − 19.5	36 → f2
20 − 24	19.5 − 24.5	24
25 − 29	24.5 − 29.5	20

Here, the maximum frequency is 50.

The class corresponding to this frequency is 9.5 - 14.5.

So, the modal class is 9.5 - 14.5.

L = Lower class limit of the modal class = 9.5

h = Class interval of the modal class = 5

f₁ = frequency of the modal class = 50

f₀ = frequency of the class preceding the modal class = 32

f₂ = frequency of the class succeeding the modal class = 36

∴ Mode = `"L" + ((f_1 − f_0)/(2 f_1 − f_0 − f_2)) × h`

= `9.5 + ((50 - 32)/(2(50) - 32 - 36)) × 5`

= `9.5 + ((18)/(100 - 68)) × 5`

= 9.5 + 0.5625 × 5

= 9.5 + 2.8125

= 12.3125 ≈ 12.31

∴ The mode of the ages of the patients is 12.31 years (approx.).