Question

The median from the following distribution is

Class:	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$	$30-35$	$35-40$	$40-45$
Frequency:	$5$	$6$	$15$	$10$	$5$	$4$	$2$	$2$

• A. $19$
• B. $19.5$
• C. $20$
• D. $18$

Answer 1

The correct option is B $19.5$

Class	Frequency	Cumulative Frequency
$5-10$	$5$	$5$
$10-15$	$6$	$11$
$15-20$	$15$	$26$
$20-25$	$10$	$36$
$25-30$	$5$	$41$
$30-35$	$4$	$45$
$35-40$	$2$	$47$
$40-45$	$2$	$49$

Now $\frac{N}{2}=24.5$.

Thus CF just more than $24.5$ is $26$. Corresponding Class is $15-20$.

$l=15$, (lower limit)

$cf=11$, (cf to class $15-20$)

$h=5$ (class size)

and $f=15$.

Hence median is

$=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$

$=15+\left(\frac{24.5-11}{15}\right)\times 5$

$=15+\left(\frac{13.5}{3}\right)$

$=15+4.5$

$=19.5$