Question

The following distribution gives the weight of $60$ students of a class.
Find the modal weight of the student :

Weight (in kg)	$40-44$	$44-48$	$48-52$	$52-56$	$56-60$	$60-64$	$64-68$	$68-72$
Number of students	$4$	$6$	$10$	$14$	$10$	$8$	$6$	$2$

Answer 1

Mode is defined as the value which occurs most frequently in a set of data

So, frequency of class $52-56$ is maximum

so $52-56$ is modal class

Lower limit $\left(l\right)$ $=52$

Class width $\left(h\right)$ $=4$

$f_1=14$

$f_0=10$

$f_2=10$

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

$=52\times \left(\frac{14-10}{2\times 14-10-10}\right)\times 4$

$=52\times \left(\frac{4}{28-20}\right)\times 4$

$=52+\frac{16}{8}$

$=52+2=54$

$\therefore$ Mode$=54$