Question

Find the median for the following distribution.

Value	$1$	$2$	$3$	$4$	$5$	$6$
$f$	$1$	$3$	$2$	$4$	$8$	$2$

Answer 1

The given data is:

Value	$f$	$cf$
$1$	$1$	$1$
$2$	$3$	$4$
$3$	$2$	$6$
$4$	$4$	$10$
$5$	$8$	$18$
$6$	$2$	$20$
	$n=20$

Here, $n$ is even.

We know that, for even number of observations, the median is the mean of ${\left(\frac{n}{2}\right)}^{th}$ and ${(\frac{n}{2}+1)}^{th}$ observation.

Hence, the median here will be the mean of ${\left(\frac{20}{2}\right)}^{th}$ and ${(\frac{20}{2}+1)}^{th}$ observation.

That is, the ${10}^{th}$ and ${11}^{th}$ observation.
From the table shown above, we can see that the tenth observation is $4$ and the eleventh observation is $5$.
Hence median $=\frac{4+5}{2}$

$=\frac{9}{2}$

$=4.5$

Hence, the median of the given data is $4.5$.