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.
Now,${\displaystyle x_k=26,h=4,f_k=25,f_k-1=20,f_k+1=22}$
∴ Mode,${\displaystyle M_0=x_k+\{ℎ\times \frac{(fk-fk-1)}{(2fk-fk-1-fk+1)}\}}$

=${\displaystyle 26+\{4\times \frac{(25-20)}{(2\times 25-20-22)}\}}$

=${\displaystyle 26+\{4\times \frac{5}{8}\}}$

= (26 + 2.5)
= 28.5