Given:
The date set is:
0,5,6,7,8,13
To find:
The outliers for the given data set.
Solution:
We have,
0,5,6,7,8,13
Divide the data in two equal parts.
(0,5,6),(7,8,13)
Divide each parenthesis in two equal parts.
(0),5,(6),(7),8,(13)
Here, first quartile is
and the third quartile is
.
The interquartile range (IQR) is:



The data lie outside the range
is called outliers.
![[Q_1-1.5IQR,Q_3+1.5IQR]=[5-1.5(3),8+1.5(3)]](https://img.qammunity.org/2022/formulas/mathematics/high-school/mkmpj745nqk3zm7yiha94va835qb4og95t.png)
![[Q_1-1.5IQR,Q_3+1.5IQR]=[5-4.5,8+4.5]](https://img.qammunity.org/2022/formulas/mathematics/high-school/beqwe8r5mbivspotxdqb7zn6vou09y291e.png)
![[Q_1-1.5IQR,Q_3+1.5IQR]=[0.5,12.5]](https://img.qammunity.org/2022/formulas/mathematics/high-school/ijybcxw18h33sziwfx573bga0lav2xrntl.png)
The data values 0 and 13 lie outside the range [0.5,12.5].
Therefore, 0 and 13 are outliers of the given data set.