Question

Given below is the distribution of total household expenditure of 200 manual workers in a city:

Expenditure (in Rs)	No. of manual workers
1000-1500	24
1500-2000	40
2000-2500	31
2500-3000	28
3000-3500	32
3500-4000	23
4000-4500	17
4500-5000	5

Find the expenditure done by maximum number of manual workers.

Answer 1

As the class 1500-2000 has the maximum frequency, it is the modal class.
$$\begin{gathered} \mathrm{Now},x_k=1500,h=500,f_k=40,f_{k-1}=24\mathrm{and}{f}_{k+1}=31 \\ \therefore \mathrm{Mode},M_0=x_k+\left\{h\times \frac{\left(f_k-f_{k-1}\right)}{\left(2f_k-f_{k-1}-f_{k+1}\right)}\right\} \\ =1500+\left\{500\times \frac{\left(40-24\right)}{\left(2\times 40-24-31\right)}\right\} \\ =1500+\left\{500\times \frac{16}{25}\right\} \\ =\left(1500+320\right) \\ =1820 \end{gathered}$$

Hence, mode = Rs 1820