Question

Find the mode of the following distribution table:

Class Interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	7	14	13	12	20	11	15	8

Answer 1

Formula for finding mode is given by,

Mode = $L+\frac{f_m-f_{m-1}}{(f_m-f_{m-1})+(f_m-f_{m+1})}\times w$

Where, L= lower class boundary of modal class

(Model class = class with highest frequency)

$f_{m-1}=$ frequency of class before modal class

$f_m=$ frequency of modal class

$f_{m+1}=$ frequency of after modal class

w = group width

Here,

0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
7	14	13	12	20	11	15	8

Hence, Mode = $40+\frac{20-12}{(20-12)+(20-11)}\times 10$

$=40+\frac{8}{8+9}\times 10$

$=40+\frac{80}{17}=40(1+\frac{2}{17})$

$=\frac{40\times 19}{17}=\frac{760}{17}$

Mode = $\frac{760}{17}$