Question

Find the median of the following data:

(ii) $72,63,29,51,35,60,55,91,85,82$

Answer 1

Find the median of the given data.

Given data: $72,63,29,51,35,60,55,91,85,82$

Arrange the observations in ascending order: $29,35,51,55,60,63,72,82,85,91$

Here, the total number of observations $\left(n\right)$ $=10$

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

$$\begin{gathered} =\frac{\left({\displaystyle \frac{10}{2}}\right)thvalue+\left({\displaystyle \frac{10}{2}+1}\right)thvalue}{2} \\ =\frac{\left({\displaystyle 5}\right)thvalue+\left({\displaystyle 5+1}\right)thvalue}{2} \\ =\frac{5thvalue+6thvalue}{2} \\ =\frac{60+63}{2} \\ =\frac{123}{2} \\ =61.5 \end{gathered}$$

Hence, the median of the given data is $61.5$.