Question

The weekly income of 600 families is tabulated below: Weekly income Number of families (in Rs) 0-1000:250 1000-2000:190 2000-3000:100 3000-4000:40 4000-5000:15 5000-6000: 5 Total 600 Compute the median income.

Answer 1

Step 1. The formula used to find the median.

The median income of $600$ families is $1263.15$

Given, the weekly income of 600 families.

To find The median income.

Formula: $\mathbf{Median}\mathbf{}\mathbf{=}\mathbf{}\mathbf{l}\mathbf{}\mathbf{+}\mathbf{}\left[\frac{\left(\frac{n}{2}-\mathrm{cf}\right)}{f}\right]\mathbf{h}$

Where, $\mathbf{l}$ is lower limit of the median class

$\mathbf{n}$ is the number of observations

$\mathrm{h}$ is the class size

$\mathbf{cf}$ is the cumulative frequency of the class preceding the median class

$\mathbf{f}$ is the frequency of the median class

Step 2. Calculate the median.

From the table,

$\frac{\mathrm{n}}{2}=\frac{600}{2}=300$

The observation lies in the class $1000-2000$

The lower limit of the class, $\mathrm{l}=1000$

Class size, $\mathrm{h}=1000$

Cumulative frequency of the class preceding the median class, $\mathrm{cf}=250$

Frequency of the median class,$\mathrm{f}=190$

$\mathrm{Median}=1000+\left[\frac{(300-250)}{190}\right]\left(1000\right)$

$=1000+\left[\frac{50}{190}\right(1000\left)\right]$

$=1000+\left[5\right(1000)/19]$

$=1000+263.15$

$=1263.15$

Therefore, the median is 1263.15