Question

Weekly income of $600$ families is given below. Find the median.

Income in $Rs$.	$0-1000$	$1000-2000$	$2000-3000$	$3000-4000$	$4000-5000$	$5000-6000$
Frequency	$250$	$190$	$100$	$40$	$15$	$5$

Answer 1

$CI$	0-1000	1000-2000	2000-3000	3000-4000	4000-5000	5000-6000
$f.i$	250	190	100	40	45	5
$c.fi$	250	440	540	580	595	600

$N=600$

Since,

$\frac{N}{2}=\frac{600}{2}$

$=300$

We know that ,

$l=1000,i=1000,F=250,f=190$

$Median=l+\frac{\frac{N}{2}-F}{f}\times i$

$=1000+\frac{\frac{600}{2}-250}{190}\times 1000$

$\begin{array}{c}=1000+\frac{50}{190}\times 1000\\ =1000+\frac{5000}{19}\\ =\frac{19000+5000}{19}\\ =\frac{24000}{19}\end{array}$

Hence,

$Median=\frac{24000}{19}=1263.15$