Question

Find the median of the following data:

(i) $31,38,27,28,36,25,35,40$

Answer 1

Find the median of the given data.

Given data: $31,38,27,28,36,25,35,40$

Arrange the observations in ascending order: $25,27,28,31,35,36,38,40$

Here, the total number of observations $\left(n\right)$ $=8$

When $n$ is even, then median $=\frac{\left({\displaystyle \frac{n}{2}}\right)thvalue+\left({\displaystyle \frac{n}{2}}+1\right)thvalue}{2}$

$$\begin{gathered} =\frac{\left({\displaystyle \frac{8}{2}}\right)thvalue+\left({\displaystyle \frac{8}{2}+1}\right)thvalue}{2} \\ =\frac{\left({\displaystyle 4}\right)thvalue+\left({\displaystyle 4+1}\right)thvalue}{2} \\ =\frac{4thvalue+5thvalue}{2} \\ =\frac{31+35}{2} \\ =\frac{66}{2} \\ =33 \end{gathered}$$

Hence, the median of the given data is $33$.