Question

Find the mean and median for the data: $4.6,3.8,2.7,3.1,4.5,4.6,3.9,0.8$

Answer 1

• The mean, (denoted by $\overline{x}$) is the average of the data.

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

$\begin{array}{rcl}\overline{x}& =& \frac{4.6+3.8+2.7+3.1+4.5+4.6+3.9+0.8}{8}\\ & =& \frac{28}{8}\\ & =& 3.5\end{array}$

• Median is the central value of the data when it is arranged in increasing or decreasing order.

Step 2: Arrange the given data in ascending order.

$0.8,2.7,3.1,3.8,3.9,4.5,4.6,4.6$

Step 3: Count the number of observations ($n$).

$n=8$

• 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.

Step 4: Here the value of $n$ is even. So substitute $n=8$ into the formula $\text{Median}=\frac{1}{2}\left[\frac{n}{2}\text{th term}+\left(\frac{n}{2}+1\right)\text{th term}\right]$.

$\begin{array}{rcl}\text{Median}& =& \frac{1}{2}\left[\frac{8}{2}\text{th term}+\left(\frac{8}{2}+1\right)\text{th term}\right]\\ & =& \frac{1}{2}\left[4\text{th term}+5\text{th term}\right]\\ & =& \frac{1}{2}\left[3.8+3.9\right]\\ & =& \frac{1}{2}\left[7.7\right]\\ & =& 3.85\end{array}$

Hence, the mean of the data is $3.5$ and the median of the data is $3.85$.