Question

Find the median for the following data shows that distance covered by $200$ people to perform their IT project.

Distance(km)	$5-15$	$15-25$	$25-35$	$35-45$
Number of people	$60$	$40$	$80$	$20$

• A. $12$ km
• B. $13$ km
• C. $14$ km
• D. $15$ km

Answer 1

The correct option is D $15$ km

Distance(km)	Number of people (f)	Cumulative frequency (cf)
$5-15$	$60$	$60$
$15-25$	$40$	$60+40=100$
$25-35$	$80$	$100+80=180$
$35-45$	$20$	$180+20=200$
	$n=\Sigma f=200$ $\frac{n}{2}=\frac{200}{2}=100$

Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$n=\Sigma f=$ Total number of frequency $=200$
$\frac{n}{2}=\frac{200}{2}=100$
So, the median class is $25-35$
L$=$ Lower limit of the median class $=25$
cf$=$ Cumulative frequency of the class preceding the median class $=180$
f$=$ Frequency of the median class $=80$
h$=$ class width$=10$
Therefore, Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$=25+\left(\frac{\frac{200}{2}-180}{10}\right)\times 10$
$=14+\left(\frac{100-180}{80}\right)\times 10$
$=25-10$
$=15$
Hence, the median is $15$km.