Question

Calculate mode from the following data:

Income	$15-24$	$25-34$	$35-44$	$45-54$	$55-64$	$65-74$
No. of workers	$8$	$10$	$15$	$25$	$25$	$20$

Answer 1

First, we will subtract $0.5$ from the lower limit of each class and add $0.5$ in the upper limit of each class to make the frequency distribution continuous.

$\text{Class Interval}$	$\text{Frequency}$
$14.5-24.5$	$8$
$24.5-34.5$	$10$
$34.5-44.5$	$15$
$44.5-54.5$	$25$
$54.5-64.5$	$25$
$64.5-74.5$	$20$

$\Rightarrow$ In given frequency table we can see two class interval has maximum frequency $25$.

$\Rightarrow$ Now, we are going to take modal class $=44.5-54.5$

Then we have, $l=44.5,f_0=15,f_1=25,f_2=25$ and $h=54.5-44.5=10$

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

$=44.5+\frac{25-15}{2\times 25-15-25}\times 10$

$=44.5+10$

$\therefore$ $\text{Mode}=54.5$