Question

What are the outliers for 0,5,6,7,8,13

Answer 1

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
`Q_1=5` and the third quartile is
`Q_3=8`.

The interquartile range (IQR) is:

`IQR=Q_3-Q_1`

`IQR=8-5`

`IQR=3`

The data lie outside the range
`[Q_1-1.5IQR,Q_3+1.5IQR]` is called outliers.

`[Q_1-1.5IQR,Q_3+1.5IQR]=[5-1.5(3),8+1.5(3)]`

`[Q_1-1.5IQR,Q_3+1.5IQR]=[5-4.5,8+4.5]`

`[Q_1-1.5IQR,Q_3+1.5IQR]=[0.5,12.5]`

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.