The following data gives the distribution of total monthly household expenditure of 200 families of a villages.

Solution:

Here, the maximum frequency is 40 so the modal class is 1500−2000.

Therefore,

$l=1500$

$h=500$

$f=40$

$f_{1}=24$

$f_{2}=33$

$\Rightarrow$ Mode $=l+\frac{f-f_{1}}{2 f-f_{1}-f_{2}} \times h$

$=1500+\frac{40-24}{80-24-33} \times 500$]

$=1500+\frac{16}{23} \times 500$

$=1500+347.83$

 

$=\operatorname{Rs} 1847.83$

Thus, the modal monthly expenditure of the families is Rs 1847.83.

Now,

Mean monthly expenditure of the families

$=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$=\frac{532500}{200}$

$=\operatorname{Rs} 2662.50 /-$

Thus, the mean monthly expenditure of the families is Rs 2662.50.