Question

Find the mode of the following distribution:

Class interval	10-14	14-18	18-22	22-26	26-30	30-34	34-38	38-42
Frequency	8	6	11	20	25	22	10	4

Answer 1

As the class 26-30 has the maximum frequency, it is the modal class.

$$\begin{gathered} \mathrm{Now},x_k=26,h=4,f_k=25,f_{k-1}=20,f_{k+1}=22 \\ \therefore \mathrm{Mode},M_0=x_k+\left\{h\times \frac{\left(f_k-f_{k-1}\right)}{\left(2f_k-f_{k-1}-f_{k+1}\right)}\right\} \\ =26+\left\{4\times \frac{\left(25-20\right)}{\left(2\times 25-20-22\right)}\right\} \\ =26+\left\{4\times \frac{5}{8}\right\} \\ =\left(26+2.5\right) \\ =28.5 \end{gathered}$$