Question

Choose whether the given statement is true or false.

"The presence of outlier in the data always changes its median."

• A. True
• B. False

Answer 1

The correct option is B False

Consider the following data which represents the scores of Adam in different games.


Here, the middle number is $8$, therefore the median of this data is $8$.

Now, assume that Adam played another game and scored $28$ in the last game.


Here, $28$ is the outlier as this value is quite different from the rest of the values of the data.

Moreover, this data set consists of $6$ games, therefore the median is calculated by taking the mean of middle two numbers, i.e.,

$\begin{array}{cc}\text{Median}& =\text{Average of middle two numbers}\\ & =\frac{8+8}{2}\\ & =\frac{16}{2}\\ & =8\end{array}$

It can be observed that the median with and without the outlier remains the same, hence the outlier does not change the value of median of the given data set.

So, the given statement is false.