Question

A football player scored the following number of goals in the $10$ matches:$1,3,2,5,8,6,1,4,7,9$ Since the number of matches is $10$ (an even number), therefore, the median $=\frac{\left[5thobservation+6thobservation\right]}{2}=\frac{8+6}{2}=7$ Is it the correct answer and why?

Answer 1

The obtained data solution in the question incorrect answer, because the data has to be ordered in either ascending or descending order before finding the median.

On arranging the data in ascending order, we obtain,

$1,1,2,3,4,5,6,7,8,9$

The number of observations is $10$, which is even.

So, median = $\frac{{\left({\displaystyle \frac{n}{2}}\right)}^{th}observation+{\left(\frac{n}{2}+1\right)}^{th}observation}{2}$

$=\frac{{\left({\displaystyle \frac{10}{2}}\right)}^{th}observation+{\left(\frac{10}{2}+1\right)}^{th}observation}{2}$

$=\frac{{\left({\displaystyle 5}\right)}^{th}observation+{\left(6\right)}^{th}observation}{2}$

$$\begin{gathered} =\frac{4+5}{2} \\ =\frac{9}{2} \\ =4.5 \end{gathered}$$

Hence, the solution given is incorrect.