Question

The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8. Find the frequency of the modal class.

Answer 1

Given, Mode = 75

Modal class = 65 – 80

Frequency of the class preceding the modal class, f₀ = 6

Frequency of class succeeding the modal class, f₂ = 8

Here, the lower limit of modal class, l = 65 and class size = 15

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

⇒ 75 = `65 + ((f_1 - 6)/(2f_1 - 6 - 8)) xx 15`

⇒ 10 = `(f_1 - 6)/(2f_1 - 14) xx 15`

⇒ `20f_1 - 140 = 15f_1 - 90`

⇒ `5f_1` = 50

⇒ `f_1` = 10

Hence, the frequency of modal class `(f_1)` is 10.