Question

Following is the data set for the number of states visited by students:
Number of States Visited by Students

31	12	0	11
13	7	4	2

Find the difference between the mean with outlier and the mean without outlier.

• A. 3

Answer 1

The correct option is A 3
In the following data set, most of the students visited the number of states in-between $0$ to $13$.

But one student visited $31$ states, which is the outlier for the data below.
Number of States Visited by Students

0	2	4	7
11	12	13	31

Mean with outlier

Sum of dataset with outlier $=80$

Number of dataset $=8$

$\therefore$ Mean without outlier
$=\frac{80}{8}$
$=10$

Given dataset without outlier:
Number of States Visited by Students

0	2	4	7
11	12	13

Mean without outlier

Sum of dataset without outlier $=49$

Number of dataset $=7$

$\therefore$ Mean without outlier
$=\frac{49}{7}$
$=7$

So, we get
$\bullet$ mean with outlier= $10$
$\bullet$ mean without outlier= $7$

Note: An outlier skews the value of the mean.

$\Rightarrow$ Mean with outlier$-$Mean without outlier
$=10-7$
$=3$