Question

Question 6
The table below shows the daily expenditure on food of 25 households in a locality.

$\begin{array}{cccccc}\text{Daily expenditure (in Rs)}& 100-150& 150-200& 200-250& 250-300& 300-350\\ \text{Number of households}& 4& 5& 12& 2& 2\end{array}$

Find the mean daily expenditure on food by a suitable method.

Answer 1

We may calculate the class mark $\left(x_i\right)$ for each interval by using the relation:

$x_i=\frac{\text{Upper class limit + lower class limit}}{2}$

Class size = 50

Now, taking 225 as assumed mean $a$, we may calculate $d_i,u_i,f_i{u}_i$ as following:

$\begin{array}{cccccc}\text{Daily expenditure (in Rs)}& f_i& x_i& d_i=x_i-225& u_i=\frac{x_i-225}{h}& f_i{u}_i\\ 100-150& 4& 125& -100& -2& -8\\ 150-200& 5& 175& -50& -1& -5\\ 200-250& 12& 225& 0& 0& 0\\ 250-300& 2& 275& 50& 1& 2\\ 300-350& 2& 325& 100& 2& 4\\ \text{Total}& 25& & & & -7\end{array}$

Now, we may observe that –

$\sum f_i=25\sum f_i{u}_i=-7Mean\overline{x}=a+\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)\times h=225+\left(\frac{-7}{25}\right)\times \left(50\right)=225-14=211$

So, mean daily expenditure on food is Rs.211.