Question

Calculate the mean and the median for the following distribution :

Number	5	10	15	20	25	30	35
Frequency	1	2	5	6	3	2	1

Answer 1

$Number$ $x_i$	$Frequency$ $f_i$	$f_i{x}_i$	$c.f$
$5$	$1$	$5$	$1$
$10$	$2$	$20$	$3$
$15$	$5$	$75$	$8$
$20$	$6$	$120$	$14$
$25$	$3$	$75$	$17$
$30$	$2$	$60$	$19$
$35$	$1$	$35$	$20$
	$\sum f_i=20$	$\sum f_i{x}_i=390$

$Mean\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{390}{20}=19.5$

Here, $N=20$

$Median=\frac{1}{2}[{\left(\frac{N}{2}\right)}^{th}term+{(\frac{N}{2}+1)}^{th}term]$

$Median=\frac{1}{2}[{\left(\frac{20}{2}\right)}^{th}term+{(\frac{20}{2}+1)}^{th}term]$

$Median=\frac{1}{2}[{10}^{th}term+{11}^{th}term]$

${10}^{th}term=20$ and ${11}^{th}term=20$

$\therefore$ $Median=\frac{1}{2}[20+20]$

$\therefore$ $Median=20$