The following data gives the distribution of total monthly household expenditure of 200
families of a village. Find the modal monthly expenditure of the families. Also, find the
mean monthly expenditure:

Expenditure	Number of families
1000-1500	24
1500-2000	40
2000-2500	33
2500-3000	28
3000-3500	30
3500-4000	22
4000-4500	16
4500-5000	7

Given data:

Modal class = 1500-2000,

l = 1500,

Frequencies:

f_m = 40 f₁ = 24, f₂ = 33 and

h = 500

Mode formula:

Mode = l+ [$\frac{f_m-f_1}{2f_m-f_1-f_2}$]×h

Substitute the values in the formula, we get

Mode =1500+[($\frac{40-24}{80-24-33}$]×500

Mode = 1500+($\frac{8000}{23}$) = 1500 + 347.83

Therefore, modal monthly expenditure of the families = Rupees 1847.83

Calculation for mean:

First find the midpoint using the formula, x_i =$\frac{upper limit+lower limit}{2}$

Let us assume a mean, A be 2750

The formula to calculate the mean,

Mean = x̄ =A +($\frac{{\displaystyle \sum _{ }}{f}_i{u}_i}{\sum _{ }{f}_i}$)×h

Substitute the values in the given formula

= 2750+($\frac{-35}{200}$)×500

= 2750-87.50

= 2662.50

So, the mean monthly expenditure of the families = Rupees 2662.50