Question

Consider the following table:

Class interval	10-14	14-18	18-22	22-26	26-30
Frequency	5	11	16	25	19

The mode of the above data is
(a) 23.5
(b) 24
(c) 24.4
(d) 25

Answer 1

(c) 24.4
The maximum frequency is 25 and the modal class is 22-26.

$$\begin{gathered} \mathrm{Now},x_k=22,f_k=25,f_{k-1}=16,f_{k+1}=19andh=4 \\ \therefore \mathrm{Mode}=x_k+h\times \left\{\frac{f_k-f_{k-1}}{2f_k-f_{k-1}-f_{k+!}}\right\} \\ =22+4\times \frac{\left(25-16\right)}{\left(2\times 25-16-19\right)} \\ =22+4\times \frac{\left(25-16\right)}{\left(50-16-19\right)} \\ =22+4\times \frac{9}{15} \\ =22+\frac{12}{5} \\ =22+2.4 \\ =24.4 \end{gathered}$$