Question

Find the mean and median for the data: $18,22,16,25,37,24,13,20,26,19$

Answer 1

Step 1: Calculate the mean by adding all the data and then dividing the sum by the number of observations in the data.

$\begin{array}{rcl}\overline{x}& =& \frac{18+22+16+25+37+24+13+20+26+19}{10}\\ & =& \frac{220}{10}\\ & =& 22\end{array}$

Step 2: Arrange the given data in ascending order.

$13,16,18,19,20,22,24,25,26,37$

$n=10$

• If $n$ is odd then, $\text{Median}=\left(\frac{n+1}{2}\right)\text{th}$ term.
• If $n$ is even then, $\text{Median}=\frac{1}{2}\left[\frac{n}{2}\text{th term}+\left(\frac{n}{2}+1\right)\text{th term}\right]$ term.

So here $\text{Median}=\frac{1}{2}\left[\frac{n}{2}\text{th term}+\left(\frac{n}{2}+1\right)\text{th term}\right]$.

$\begin{array}{rcl}\text{Median}& =& \frac{1}{2}\left[\frac{10}{2}\text{th term}+\left(\frac{10}{2}+1\right)\text{th term}\right]\\ & =& \frac{1}{2}\left[5\text{th term}+6\text{th term}\right]\\ & =& \frac{1}{2}\left[\mathrm{20}+\mathrm{22}\right]\\ & =& \frac{1}{2}\left[42\right]\\ & =& 21\end{array}$

Hence, the mean of the data is $22$ and the median of the data is $21$.