# How to Calculate 3 Sigma - Formula, Example

## How to Calculate 3 Sigma - Definition

##### Definition:

This tutorial explains how to calculate the three sigma values.

#### Formula:

Avg = Dataset / N S = Dataset - Avg; [list of values] Square = S2; [list of values] Avgnew+ = Square Variance = Avgnew / N; Sigma = √variance Threesigma= 3 * sigma Where, Avg = Average N = Total number of data set DataSet = List of values
##### Example :

The following are the points obtained by the set of 5 players in a game 11,10,9,10.2,15.7. Find the variance and 3sigma for the given points.

##### Given :

Data Set = 11,10,9,10.2,15.7 N = 5

##### To Find :

Variance and Three sigma

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

First, let us calculate the average for the given data set. Avg = Dataset/N = 11+10+9+10.2+15.7 / 5 = 55.9 / 5 Avg = 11.18

###### Step 2:

S,Square and AvergeNew value can be calcuated in the below table

SSquareAvgnew
-0.180.0320.0324
-1.181.3921.4248
-2.184.7526.1772
-0.980.9607.1376
4.5120.4327.5679
###### Step 3:

Let us calculate the value of variance. Variance = Avgnew/N; Variance = 5.5136 Sigma = √variance= √5.5136 Three sigma = 3*sigma 3sigma = 7.0443

##### Result :

Three sigma = 7.0443