Question

For the following data obtain the mode.

Weight (in kg)	$21-25$	$26-30$	$31-35$	$36-40$	$41-45$	$46-50$	$51-55$	$56-60$
No. of students	$5$	$4$	$3$	$18$	$20$	$14$	$8$	$3$

Answer 1

Highest frequency=highest number of students in a class$=20$

Given intervals are closed intervals. To make them open intervals, subtract $0.5$ from lower boundary and add the same in the upper boundary.

Now, modal class$=40.5-45.5$

$l=40.5;h=5;f_m=20;f_{m-1}=18;f_{m+1}=14$

mode$=L+\frac{f_m-f_{m-1}}{2f_m-f_{m-1}-f_{m+1}}\times n$

$=40.5+\frac{2}{2+6}\times 5$

$=41.75$ kg