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

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

Here, $\sum f_i=20$ and $\sum f_i{x}_i=390$

$Mean=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{390}{20}=19.5$

Here, $N=20$ then, $\frac{N}{2}=\frac{20}{2}=10$

$\therefore$ Median $=20$