The mean of the following frequency distribution is 50 but the frequencies f₁ and f₂ in classes 20 - 40 and 60 - 80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.

First, we calculate the class mark of given data

Given that, sum of all frequencies = 120

Here,

assumed mean, a = 50 and

class width, h = 20

By step deviation method,

⇒ 4 + f₂ - f₁ = 0

⇒ -f₂ + f₁ = 4 - - - - (ii)

On adding Eqs. (i) and (ii), we get

2f₁ = 56

⇒ f₁ = 28

Put the value of in Eq. (i), we get

f₂ = 52 - 28

⇒ f₂ = 24

Hence, f₁ = 28 and f₂ = 24