Question

Following is the data set for the number of states visited by students:


$\text{Mean with outlier}-\text{Mean without outlier}=$

Answer 1

In the following data set, most of the students visited the number of states in-between $1$ to $10$. But one student visited $19$ states, which is the outlier for the data below.


Mean with outlier
Sum of dataset with outlier $=64$
Number of dataset $=16$
$\therefore$ Mean without outlier
$=\frac{64}{16}$
$=4$
Given dataset without outlier:
Mean without outlier
Sum of dataset without outlier $=45$
Number of dataset $=15$
$\therefore$ Mean without outlier
$=\frac{45}{15}$
$=3$
So, we get
$\bullet$ mean with outlier= $4$
$\bullet$ mean without outlier= $3$
Note: An outlier skews the value of the mean.
$\Rightarrow$ Mean with outlier$-$Mean without outlier
$=4-3$
$=1$