The mean of the following frequency distribution is 57.6 and the sum of the frequencies is 50. Find the missing frequencies f₁ and f₂ :

Now,

[given: ∑f_i = 50]

⇒ 57.6(50) = 1940 + 30f₁ +70f₂

⇒ 2880 = 1940 + 30f₁ +70f₂

⇒ 2880 – 1940 = 30f₁ +70f₂

⇒ 940 = 30f₁ +70f₂

⇒ 94 = 3f₁ +7f₂ …(i)

and 32 + f₁ +f₂ = 50

⇒ f₁ +f₂ = 50 – 32

⇒ f₁ +f₂ = 18

⇒ f₁ = 18 – f₂ …(ii)

Now, putting the value of f₁ in eq. (i), we get

3(18 –f₂) + 7f₂ = 94

⇒ 54 – 3f₂ + 7f₂ = 94

⇒ 4f₂ = 94 – 54

⇒ 4f₂ = 40

⇒ f₂ = 10

Now, substitute the value of f₂ in eq. (ii), we get

f₁ = 18 – 10

⇒ f₁ = 8