Question

Find the median of the following data:

$24,26,16,16,21,17,30,28$

Answer 1

Step 1: First we arrange the given data in ascending order.

Given , $24,26,16,16,21,17,30,28$

$16,16,17,21,24,26,28,30$

Here, total number of observations $=8$

Step 2: Finding the median:

Since, $8$ is an even number

$\therefore Median=\left(\frac{{\left({\displaystyle \frac{n}{2}}\right)}^{th}observation+{\left({\displaystyle \frac{n}{2}+1}\right)}^{th}observation}{2}\right)$, where, $n$ is total number of observations

$=\left(\frac{{\left({\displaystyle \frac{8}{2}}\right)}^{th}+{\left({\displaystyle \frac{8}{2}+1}\right)}^{th}}{2}\right)$

$=\frac{4thobservation+5thobservation}{2}$

$=\frac{21+24}{2}$

$$\begin{gathered} =\frac{45}{2} \\ =22.5 \end{gathered}$$

Hence, the median of the given data is $22.5$.