Question

The mode of the following frequency distribution is 36. Find the missing frequency (f).

Class	Frequency
0 - 10	8
10 - 20	10
20 - 30	f
30 - 40	16
40 - 50	12
50 - 60	6
60 - 70	7

Answer 1

Here, Modal Class = 30 – 40

So, f₀ = f, f₁ = 16, f₂ = 12, l = 30 and h = 10

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

⇒ `36 = 30 + (16 - f)/(2 xx 16 - f - 12) xx 10`

⇒ `6 = (16 - f)/(20 - f) xx 10`

⇒ 120 – 6f = 160 – 10f

⇒ 4f = 40

⇒ f = 10