Question:
The following tables gives the distribution of total household expenditure (in rupees) of manual workers in a city.
Find the average expenditure (in rupees) per household
Solution:
Given:
Let the assumed mean be A = 275 and h = 50.
We know that mean, $\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$
Now, we have $N=\sum f_{i}=200, \sum f_{i} u_{i}=-35, h=50$ and $A=275$.
Putting the values in the above formula, we get
$\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$
$=275+50\left(\frac{1}{200} \times(-35)\right)$
$=275-\frac{1750}{200}$
$=275-8.75$
$=266.25$
Hence, the average expenditure (in Rs.) per household is $266.25$.