Let’s draw the table and calculate the relative value of variables ∑xi×fi

We have,

∑f_i = 120 (given)

∑f_i = 68 + f₁ + f₂ = 120

f₁ + f₂ = 120 - 68

f₁ + f₂ = 52…. Equation (i)

Now we have,

Mean = 50 (given)

Mean = = 50

50 =

50×68 + f₁ + f₂ = 3480 + 30f₁ + 70f₂

3400 + 50 f₁ + 50f₂ = 3480 + 30f₁ + 70f₂

50f₁ - 30f₁ + 50 f₂ -70f₂ = 3480 – 3400

20f₁-20f₂ = 80

20(f₁-f₂) = 80

f₁-f₂ = ……. Equation (ii)

by adding equation (i) and (ii) we get,

∑f₁ = 56

From equation (ii)

f₁-f₂ = 4

28 – f₂ = 4

f₂ = 28-4 = 24

Hence missing frequencies are f₁ = 28 and f₂ = 24.