Question

Find the median of $17,23,36,12,18,23,40$ and $20$.

Answer 1

Calculate the median of the given numbers

Given numbers: $17,23,36,12,18,23,40$ and $20$.

Arrange the numbers in ascending order: $12,17,18,20,23,23,36,40$.

The number of terms, $n=8$.

Let $n^{\mathrm{th}}$ term be denoted by $t_n$.

As the number terms in even, thus the median will be $\frac{{\mathbf{t}}_{\frac{n}{2}}\mathbf{+}{\mathbf{t}}_{\frac{\mathit{n}}{\mathbf{2}}\mathbf{+}\mathbf{1}}}{\mathbf{2}}$

Substitute $n$ with $8$.

$\frac{t_{\left(\frac{8}{2}\right)}+t_{\left(\frac{8}{2}+1\right)}}{2}=\frac{\left\{t_4+t_5\right\}}{2}$

Substitute $t_4$ with $20$ and $t_5$ with $23$.

Median $=\frac{\left(20+23\right)}{2}=\frac{43}{2}=21.5$.

Therefore, the median of the given numbers is $21.5$.