Question

Given below is the data set for the number of states visited by students.


What is the difference between median with outlier and median without outlier?

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is D $0$

In the given data set, except $19$, all the remaining data points lie in between $0$ to $10$. So, the outlier of the given data set is $19$.

On arranging the data points with outlier in increasing order, we get


Median with outlier= Mean of $8^{\text{th}}\text{and}{9}^{\text{th}}$ data points

$=\frac{3+3}{2}=3$

Given ordered data set without outlier:


Median without outlier= Central value of the data set $=3$

So, we get
$\bullet$ median with outlier= $3$
$\bullet$ median without outlier= $3$

$\therefore \text{Median with Outlier}-\text{Median without outlier}$$=3-3=0$, i.e., option (d.) is the correct one.

$\underset{–}{\text{Note:}}$ For the given data set, an outlier does not shift the median.