Question

The table shows the salaries of $280$ persons.

Salary(In thousand)	No. of Persons
$5-10$	$49$
$10-15$	$133$
$15-20$	$63$
$20-25$	$15$
$25-30$	$6$
$30-35$	$7$
$35-40$	$4$
$40-45$	$2$
$45-50$	$1$

Calculate the median salary of the data.

Answer 1

Salary(In thousand)	Frequency$\left(f\right)$ Cumulative frequency$\left(cf\right)$
$5-10$	$49$ $49$
$10-15$	$133$ $182$
$15-20$	$63$ $245$
$20-25$	$15$ $260$
$25-30$	$6$ $266$
$30-35$	$7$ $273$
$35-40$	$4$ $277$
$40-45$	$2$ $279$
$45-50$	$1$ $280$

Total no. of persons $N=49+133+63+15+6+7+4+2+1=280$

Now, $\frac{N}{2}=140$

$cf\ge \frac{N}{2}$ is $182$

Median class is $10-15$

$f=133$

Lower limit of median class $l=10$

$c.f.$ above the median class is $49$

Width of the interval $h=5$

Median $=l+\left(\frac{\frac{N}{2}-c.f}{f}\right)h$

$=10+\left(\frac{140-49}{133}\right)5=10+\frac{91}{133}\times 5=13.42$

Hence, median $=13.42$