Question

Estimate the median for the following data given below$:$

Marks	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$
Students	$50$	$40$	$30$	$20$	$10$

• A. $53.25$
• B. $55.25$
• C. $58.125$
• D. $63.125$

Answer 1

Answer: (C)

$58.125$

Marks	Students (f)	Cumulative frequency (cf)
$50-55$	$50$	$50$
$55-60$	$40$	$50+40=90$
$60-65$	$30$	$90+30=120$
$65-70$	$20$	$120+20=140$
$70-75$	$10$	$140+10=150$

Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$n=\Sigma f=$ Total number of frequency $=150$
$\frac{n}{2}=\frac{150}{2}=75$
So, the median class is $55-60$
L$=$ Lower limit of the median class $=55$
cf$=$ Cumulative frequency of the class preceding the median class $=50$
f$=$ Frequency of the median class $=40$
h$=$ class width$=5$
Therefore, Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$=55+\left(\frac{\frac{150}{2}-50}{40}\right)\times 5$
$=55+\left(\frac{75-50}{40}\right)\times 5$
$=55+\frac{25}{8}$
$=58.125$
Hence, the median is $58.125$.