In the following table, Σf = 200 and mean = 73. Find the missing frequencies f₁ and f₂.

x	f
0	46
50	f1
100	f2
150	25
200	10
250	5

Given,

⇒ Σf = 200

⇒ 86 + f₁ + f₂ = 200

⇒ f₁ + f₂ = 200 - 86

⇒ f₁ + f₂ = 114

⇒ f₁ = 114 - f₂ ……..(1)

Given, mean = 73

$\Rightarrow \dfrac{Σfx}{Σf} = 73 \\[1em] \Rightarrow \dfrac{7000 + 50f$1 + 100f2}{86 + f1 + f2} = 73 \\[1em] \Rightarrow \dfrac{7000 + 50f1 + 100f2}{86 + 114} = 73 \\[1em] \Rightarrow 7000 + 50f1 + 100f2 = 200 \times 73 \\[1em] \Rightarrow 7000 + 50(f1 + 2f2) = 14600 \\[1em] \Rightarrow 50(f1 + 2f2) = 14600 - 7000 \\[1em] \Rightarrow 50(f1 + 2f2) = 7600 \\[1em] \Rightarrow f1 + 2f2 = \dfrac{7600}{50} \\[1em] \Rightarrow f1 + 2f2 = 152 \\[1em] \Rightarrow 114 - f2 + 2f2 = 152 \text{ (From 1)}\\[1em] \Rightarrow 114 + f2 = 152 \\[1em] \Rightarrow f2 = 152 - 114 \\[1em] \Rightarrow f_2 = 38.

Substituting value of f₂ in (1), we get :

⇒ f₁ = 114 - f₂ = 114 - 38 = 76.

Hence, f₁ = 76 and f₂ = 38.