Question

The five number summary of a dataset is given as

0, 4, 12, 14, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______


The five number summary of a dataset is given as
2, 8, 14, 18, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______

.
.

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.