The daily expenditure of 100 families are given below. Calculate f₁ and f₂, if the mean daily expenditure is ₹188.

Expenditure (in ₹)	No. of families
140 - 160	5
160 - 180	25
180 - 200	f1
200 - 220	f2
220 - 240	5

We construct the table as under :

As there are 100 families,

∴ 35 + f₁ + f₂ = 100
⇒ f₁ + f₂ = 100 - 35 = 65
⇒ f₁ = 65 - f₂      ……(i)

$\text{Mean} = \dfrac{Σf$iui}{Σfi} \\[1em] \Rightarrow 188 = \dfrac{6150 + 190f1 + 210f2}{35 + f1 + f2} \\[1em] \Rightarrow 188(35 + f1 + f2) = 6150 + 190f1 + 210f2 \\[1em] \Rightarrow 188(35 + 65 - f2 + f2) = 6150 + 190(65 - f2) + 210f2 \text{ …….(Using (i))} \\[1em] \Rightarrow 188(100) = 6150 + 12350 - 190f2 + 210f2 \\[1em] \Rightarrow 18800 = 18500 + 20f2 \\[1em] \Rightarrow 18800 - 18500 = 20f2 \\[1em] \Rightarrow 20f2 = 300 \\[1em] \Rightarrow f_2 = 15.

Using (i),

⇒ f₁ = 65 - f₂ = 65 - 15 = 50.

Hence, f₁ = 50 and f₂ = 15.