Question

The monthly income of $100$ families are given as below : Income$(inRs)$ Number of families $0-5000:85000-10000:2610000-15000:4115000-20000:1620000-25000:325000$-$30000:330000-35000:235000-40000:1$ Calculate the modal income.

Answer 1

Calculate the modal income.

Given,

The monthly income of $100$families.

Income$(inRs)$	Number of families
$0-5000$	$8$
$5000-10000$	$26$
$10000-15000$	$41$
$15000-20000$	$16$
$20000-25000$	$3$
$25000-30000$	$3$
$30000-35000$	$2$
$35000-40000$	$1$

According to the data provided,

The highest frequency is $41$

$41$lies in interval $10000-15000$

Here,

$I=10000,f_m=41,f_1=26,f_2=16andh=5000$

∴ $I+\left(\frac{f_m-f_1}{2f_m-f_1-f_2}\right)\times h$

$=10000+\left(\frac{41-26}{2\times 41-26-16}\right)\times 5000$

$=10000+\left(\frac{15}{82-42}\right)\times 5000$

$=10000+\left(\frac{15}{40}\right)\times 5000$

$=10000+15\times 125$

$=10000+15\times 125$

$=10000+1875$

$=11875$

As a result, the modal monthly income is $Rs.11875$.