# Statistics Outlier Function – lesscss

By | April 24, 2019

# Statistics – Outlier Function

An outlier in a probability distribution function is a number
that is more than 1.5 times the length of the data set away from
either the lower or upper quartiles. Specifically, if a number is
less than \${Q_1 – 1.5 times IQR}\$ or greater than \${Q_3 + 1.5
times IQR}\$, then it is an outlier.

Outlier is defined and given by the following probability
function:

## Formula

\${Outlier datas are, lt Q_1 – 1.5 times IQR (or) gt Q_3
+ 1.5 times IQR }\$

Where −

• \${Q_1}\$ = First Quartile

• \${Q_2}\$ = Third Quartile

• \${IQR}\$ = Inter Quartile Range

### Example

Problem Statement:

Consider a data set that represents the 8 different students
15, 3, 16, 25, 12 and 14. Discover the outlier data from the

Solution:

Given data set is:

 11 13 15 3 16 25 12 14

Arrange it in ascending order:

 3 11 12 13 14 15 16 25

First Quartile Value() \${Q_1}\$

\${ Q_1 = frac{(11 + 12)}{2} \[7pt] = 11.5 }\$

Third Quartile Value() \${Q_3}\$

\${ Q_3 = frac{(15 + 16)}{2} \[7pt] = 15.5 }\$

Lower Outlier Range (L)

\${ Q_1 – 1.5 times IQR \[7pt] = 11.5 – (1.5 times 4)
\[7pt] = 11.5 – 6 \[7pt] = 5.5 }\$

Upper Outlier Range (L)

\${ Q_3 + 1.5 times IQR \[7pt] = 15.5 + (1.5 times 4)
\[7pt] = 15.5 + 6 \[7pt] = 21.5 }\$

In the given information, 5.5 and 21.5 is more greater than the
other values in the given data set i.e. except from 3 and 25
since 3 is greater than 5.5 and 25 is lesser than 21.5.

In this way, we utilize 3 and 25 as the outlier values.

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