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Outlier Function
Statistics - Outper Function
An outper in a probabipty 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 ${Q_1 - 1.5 imes IQR}$ or greater than ${Q_3 + 1.5 imes IQR}$, then it is an outper.
Outper is defined and given by the following probabipty function:
Formula
${Outper datas are, lt Q_1 - 1.5 imes IQR (or) gt Q_3 + 1.5 imes IQR }$
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 periodic task count. The task count information set is, 11, 13, 15, 3, 16, 25, 12 and 14. Discover the outper data from the students periodic task counts.
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 Outper Range (L)
${ Q_1 - 1.5 imes IQR \[7pt] = 11.5 - (1.5 imes 4) \[7pt] = 11.5 - 6 \[7pt] = 5.5 }$
Upper Outper Range (L)
${ Q_3 + 1.5 imes IQR \[7pt] = 15.5 + (1.5 imes 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 utipze 3 and 25 as the outper values.
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