---
title: "Variance"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574926/Variance"
format: markdown
---
# Variance V

 

The variance is a measure of how much the probability distribution is spread from the mean:

 

![image](media://5ebc688f-e678-4aa7-9f42-016f1ba2b39d)

> Macro (mathblock)

 

where 

![image](media://9d778326-16af-4c9d-8710-3103f3857107)

 > Macro (inline-media-image)

 denotes the expected value ([mean](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574925/)) of whatever is in the brackets, so:

 

![image](media://688ac0db-b4e2-4683-ad20-749e12923e1d)

> Macro (mathblock)

 

The variance sums up the squared distance from the mean of all possible values of *x*, weighted by the probability of *x* occurring. The variance is known as *the second moment about the mean*. It has units that are the square of the units of *x*. So, if *x* is cows in a random field, *V* has units of cows2. This limits the intuitive value of the variance.

 

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

 

|  |  |  |
| --- | --- | --- |
| ![image](media://9110937b-003f-441e-9388-0febecef8ec2)<br>> Macro (mathinline) | and | ![image](media://cf69beae-cffe-45dd-94c1-73dced7563a6)<br>> Macro (mathinline) |

|  |  |  |
| --- | --- | --- |
| ![image](media://b1e03f2f-cd39-4cd7-9f70-8d66d307ec78)<br>> Macro (mathinline) | and | ![image](media://00980281-0bff-4fb9-87b7-a707c5ffb245)<br>> Macro (mathinline) |

|  |  |
| --- | --- |
| ![image](media://c38eb5f4-94f7-4d8a-a361-a67bca3607f5)<br>> Macro (mathblock) | providing the *Xi*s are uncorrelated. |

 

 

 

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