---
title: "Standard deviation"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574927/Standard%20deviation"
format: markdown
---
# Standard deviation *s*

  


The standard deviation is the positive square root of the variance, i.e. s = √*V*. Thus, if the variance has units of cows<sup>2</sup>, the standard deviation has units of cows, the same as the variable x. The standard deviation is therefore more popularly used to express a measure of spread.

### ***Example***

The variance *V* of the Uniform(1,3) distribution is calculated as follows:

  


                        

|  |  |  |
| --- | --- | --- |
| ![image](media://2e6bfa5d-c959-4014-9535-c622c36fdafb)<br>> Macro (mathblock) | ![image](media://6f104b31-ee78-4d1d-9209-79d1109f55f3)<br>> Macro (mathinline) | from [here](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574925/) |

           

and therefore

![image](media://73439203-237d-40f3-9544-8d61dbc5bbb9)

  


> Macro (mathblock)

  


and the standard deviation *s* is therefore:

![image](media://40564041-526a-4ead-8964-3b221fece5c4)


> Macro (mathblock)

  


Variance and standard deviation have the following properties, where *a* is some constant and X, Xi are random variables:

  


|  |  |  |
| --- | --- | --- |
| ![image](media://4fd280b4-34b4-4833-ace0-eae782378d35)<br>> Macro (mathinline) | and | ![image](media://3939ade1-db62-4a5c-97f1-700018264511)<br>> Macro (mathinline) |

  


|  |  |  |
| --- | --- | --- |
| ![image](media://c7652072-ec91-4c4f-8e80-ff5d30390c05)<br>> Macro (mathinline) | and | ![image](media://27c85b15-b9d9-4456-9c0e-5df2bbc68b22)<br>> Macro (mathinline) |

  


|  |  |
| --- | --- |
| ![image](media://5e9407eb-5608-425c-9940-13f9ee11ab67)<br>> Macro (mathblock) | providing the *Xi*s are uncorrelated. |

  


  


  


  


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