Question

The monthly income of 100 families are given as below:

Income (in Rs)	Number of families
0 – 5000	8
5000 – 10000	26
10000 – 15000	41
15000 – 20000	16
20000 – 25000	3
25000 – 30000	3
30000 – 35000	2
35000 – 40000	1

Calculate the modal income.

Answer 1

In a given data, the highest frequency is 41, which lies in the interval 10000 – 15000.

Here, l = 10000, f_m = 41, f₁ = 26, f₂ = 16 and h = 5000

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

= `10000 + ((41 - 26)/(2 xx 41 - 26 - 16)) xx 5000`

= `10000 + (15/(82 - 42)) xx 5000`

= `10000 + (15/40) xx 5000`

= 10000 + 15 × 125

= 10000 + 1875

= ₹ 11875

Hence, the modal income is ₹ 11875.