The mean of the following distribution is 62.8 and the sum of all the frequencies is 50. Find the missing frequencies f₁ and f₂.

Class	Frequency
0 - 20	5
20 - 40	f1
40 - 60	10
60 - 80	f2
80 - 100	7
100 - 120	8

By formula,

Class mark = $\dfrac{\text{Upper limit + Lower limit}}{2}$

Given,

Sum of frequencies = 50

⇒ f₁ + f₂ + 30 = 50

⇒ f₁ + f₂ = 20

⇒ f₁ = 20 - f₂ ……..(1)

By formula,

Mean = $\dfrac{Σfx}{Σf}$

⇒ 62.8 = $\dfrac{2060 + 30f$1 + 70f2}{50}

⇒ 2060 + 30f₁ + 70f₂ = 3140

⇒ 30f₁ + 70f₂ = 1080

Substituting value of f₁ in above equation from (1), we get :

⇒ 30(20 - f₂) + 70f₂ = 1080

⇒ 600 - 30f₂ + 70f₂ = 1080

⇒ 40f₂ = 480

⇒ f₂ = $\dfrac{480}{40}$ = 12.

⇒ f₁ = 20 - f₂ = 20 - 12 = 8.

Hence, f₁ = 8 and f₂ = 12.