Question

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.
$\begin{array}{cccc}\text{Expenditure}& \text{Frequency}& \text{Expenditure}& \text{Frequency}\\ \left(\text{in rupees}\right)\left(x_i\right)& \left(f_i\right)& \left(\text{in rupees}\right)\left(x_i\right)& \left(f_i\right)\\ 100-150& 24& 300-350& 30\\ 150-200& 40& 350-400& 22\\ 200-250& 33& 400-450& 16\\ 250-300& 28& 450-500& 7\end{array}$
Find the average expenditure (in rupees) per household.

Answer 1

Given:

Let the assumed mean be A = 275 and h = 50.

We know that mean, $\overline{X}=A+h(\frac{1}{N}{\sum }_{i=1}^n{f}_i{u}_i)$

Now, we have $N=\sum f_i=200,\sum f_i{u}_i=-35$.

Putting the values in the above formula, we get

$\overline{X}=A+h(\frac{1}{N}{\sum }_{i=1}^n{f}_i{u}_i)$

$=275+50(\frac{1}{200}\times (-35))$

$=275-\frac{1750}{200}$

$275-8.75=266.25$

Hence, the average expenditure (in Rs) per household is 266.25.