# Learn How to Use Outlier Function in Probability - Definition, Formula, Example

## Learn How to Use Outlier Function in Probability - Formula, Example

##### Definition:

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 Q1 - 1.5xIQR or greater than Q3 + 1.5xIQR, then it is an outlier.

#### Formula:

Outlier datas are, < Q1 - 1.5xIQR (or) > Q3 + 1.5xIQR
###### Where,

Q1 = First Quartile Q3 = Third Quartile IQR = Inter Quartile Range

##### Example :

Consider a data set that represents the 8 different students periodic task counts. The task count data set is, 11, 13, 15, 3, 16, 25, 12, 14. Find out the outlier datas from the students periodic task counts.

##### Solution :
###### Step : 1

First, write down the given data set 11, 13, 15, 3, 16, 25, 12, 14 Then, arrange it in Ascending order 3, 11, 12, 13, 14, 15, 16, 25

###### Step : 2

First Quartile Value (Q1) = (11 + 12) / 2 = 11.5 Third Quartile Value (Q3) = (15 + 16) / 2 = 15.5

###### Step : 3

Lower Outlier Range (L) = Q1 - 1.5 x IQR = 11.5 - (1.5 x 4) = 11.5 - 6 = 5.5 Upper Outlier Range (U) = Q3 + 1.5 x IQR = 15.5 + (1.5 x 4) = 15.5 + 6 = 21.5 In the given data, 5.5 and 21.5 is greater than all the other values in the given data set i.e except 3 and 25 since 3 is greater than 5.5 and 25 is lesser than 21.5. So, we use 3 and 25 as the outlier values.

##### Result :

Outlier data are, 3,25 from the given students periodic task data set. Outlier probability function is calculated using Interquartile Range, first quartile (Q1) and third quartile (Q3).