Question

The marks in the science of $80$ students of class X are given below: Find the mode of the marks obtained by the students in science.

Marks:	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency:	$3$	$5$	$16$	$12$	$13$	$20$	$5$	$4$	$1$	$1$

Answer 1

Marks	Frequency
0-10	3
10-20	5
20-30	16
30-40	12
40-50	13
50-60	20
60-70	5
70-80	4
80-90	1
90-100	1
	N = 80

As frequency is maximum for the class $50-60$, modal class is $50-60$.

$Mode=l+\frac{f_1-f_0}{2f_1-(f_0+f_2)}\times h$

where,

$l=$ lower limit of modal class $=50$

$f_1=$ frequency of modal class $=20$

$f_0=$ frequency of class preceeding the modal class $=13$

$f_2=$ frequency of class succeeding the modal class $=5$

$h=$ higher limit - lower limit $=60-50=10$

$Mode=50+\frac{20-13}{2\times 20-(13+5)}\times 10$

$mode=50+\frac{7}{22}\times 10$

$=50+3.18$

$=53.18$