Question

Find mode for the following data.

Employees salary	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
No. of employees	$10$	$12$	$18$	$8$	$9$	$5$	$6$	$4$

Answer 1

$Class$	$Frequency$
$0-10$	$10$
$10-20$	$12$
$20-30$	$18$
$30-40$	$8$
$40-50$	$9$
$50-60$	$5$
$60-70$	$6$
$70-80$	$4$

Here the maximum frequency is $18$ then the corresponding class $20-30$ is the modal class.

$l=20,h=30-20=10,f=18,f_1=12,f_2=8$

$Mode=l+\frac{f-f_1}{2f-f_1-f_2}\times h$

$=20+\frac{18-12}{2\left(18\right)-12-8}\times 10$

$=20+\frac{6}{16}\times 10$

$=20+\frac{15}{4}$

$=20+3.75$

$\therefore$ $Mode=23.75$