The following data gives the distribution of total monthly household expenditure of 200 families of a village.
Question:
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:
Solution:
Modal class $=1500-2000$
Mode $=\ell+\left\{\frac{\mathbf{f}-\mathbf{f}_{\mathbf{0}}}{\boldsymbol{2} \mathbf{f}-\mathbf{f}_{\mathbf{0}}-\mathbf{f}_{\mathbf{2}}}\right\} \times \mathrm{h}$
$=1500+\left\{\frac{\mathbf{4 0}-\mathbf{2 4}}{\mathbf{2} \times \mathbf{4 0}-\mathbf{2 4}-\mathbf{3 3}}\right\} \times 500$
$=1500+\frac{\mathbf{1 6}}{\mathbf{8 0}-\mathbf{5 7}} \times 500=1847.83$