Formula for Mode with Examples

Here you will learn what is the formula for mode of grouped and ungrouped data and how to find mode with examples.

Let’s begin –

What is Mode ?

Mode is the size of the variable which occurs most frequently.

Formula for Mode :

(i) For ungrouped distribution : The value of that variate which is repeated maximum number of times.

Example : Find the mode of the following data 1, 2, 3, 1, 5, 6, 2, 8, 2, 9.

Solution : Here, 2 is repeated maximum number of times.

Hence, Mode is 2.

(ii) For ungrouped frequency distribution : The value of that variate which have maximum frequency.

Example : Find the mean of the following freq. dist.

Size of the shoes	4	5	6	7	8
Number of pairs sold	10	15	20	35	16

Solution : In the above table we notice that the size 7 has the maximum frequency i.e. 35

Therefore, 7 is the mode of distribution.

(iii) For grouped frequency distribution : First we find the class which have maximum frequency, this is model class.

$\therefore$ Mode = ($l$ + $f_0 – f_1\over {2f_0 – f_1 – f_2}$)$\times$h

where  $l$ = lower limit of model class

$f_0$ = freq. of model class

$f_1$ = freq. of the class preceding model class

$f_2$ = freq. of the class succeeding model class

h = class interval of model class

Example : Find the mean of the following freq. dist.

Size of the shoes	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Number of pairs sold	2	18	30	45	35	20	6	3

Solution : Here the class 30-40 has maximum frequency, so this is the modal class

$l$ = 30, $f_0$ = 45, $f_1$ = 30, $f_2$ = 35, h = 10

$\therefore$ Mode = ($l$ + $f_0 – f_1\over {2f_0 – f_1 – f_2}$)$\times$h = $45 – 30\over 2\times 45 – 30 – 35$$\times$ 10 = 36