Question

Calculate the mode from the following data:

Monthly salary (in Rs)	No. of employees
0-5000	90
5000-1000	150
10000-15000	100
15000-20000	80
20000-25000	70
25000-30000	10

Answer 1

As the class 5000-10000 has the maximum frequency, it is the modal class.

$$\begin{gathered} \mathrm{Now},x_k=5000,h=5000,f_k=150,f_{k-1}=90\mathrm{and}{f}_{k+1}=100 \\ \therefore \mathrm{Mode},M_0=x_k+\left\{h\times \frac{\left(f_k-f_{k-1}\right)}{\left(2f_k-f_{k-1}-f_{k+1}\right)}\right\} \\ =5000+\left\{5000\times \frac{\left(150-90\right)}{\left(2\times 150-90-100\right)}\right\} \\ =5000+\left\{5000\times \frac{60}{110}\right\} \\ =\left(5000+2727.27\right) \\ =7727.27 \end{gathered}$$

Hence, mode = Rs 7727.27