Question

Find the median of the following data :

$10,8,2,4,3,5,1,7,6,9$

Answer 1

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

Given , $10,8,2,4,3,5,1,7,6,9$

$1,2,3,4,5,6,7,8,9,10$

Here, total number of observations $=10$

Since, $10$ is an even number

Median is the average of $\left(\frac{n}{2}\right)th$and $\left(\frac{n}{2}+1\right)th$observation.

Step 2: Find the median

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

$=\left(\frac{\left({\displaystyle \frac{10}{2}}\right)+\left({\displaystyle \frac{10}{2}+1}\right)}{2}\right)th$

$=\frac{5thobservation+6thobservation}{2}$

$=\frac{5+6}{2}$ observation

$$\begin{gathered} =\frac{11}{2} \\ =5.5 \end{gathered}$$

Hence, the median of the given data is $5.5$.