Question

The five number summary of a dataset is given as

Answer 1

Given:

The five number summary of two data sets are given as:

a) 0, 4, 12, 14, 20

b) 2, 8, 14, 18, 20

To find:

The range for the outliers.

Solution:

We know that,

An observation is considered an outlier if it is below $Q_1-1.5(IQR)$

An observation is considered an outlier if it is above $Q_3+1.5(IQR)$

Where, IQR is the interquartile range and $IQR=Q_3-Q_1$.

The five number summary of two data sets are given as:

0, 4, 12, 14, 20

Here, $Q_1=4$ and $Q_3=14$.

Now,

$IQR=14-4$

$IQR=10$

The range for the outliers is:

$[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)]$

$[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15]$

$[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29]$

An observation is considered an outlier if it is below -11.

An observation is considered an outlier if it is above 29.

The five number summary of two data sets are given as:

2, 8, 14, 18, 20

Here, $Q_1=8$ and $Q_3=18$.

Now,

$IQR=18-8$

$IQR=10$

The range for the outliers is:

$[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)]$

$[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15]$

$[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33]$

An observation is considered an outlier if it is below -7.

An observation is considered an outlier if it is above 33.