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).

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