# Difference between revisions of "FAQ"

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''σ'' ("sigma") is a single number that characterizes precision. In statistics ''σ'' represents [http://en.wikipedia.org/wiki/Standard_deviation standard deviation], which is a measure of dispersion, and which is a parameter for the [http://en.wikipedia.org/wiki/Normal_distribution normal distribution]. | ''σ'' ("sigma") is a single number that characterizes precision. In statistics ''σ'' represents [http://en.wikipedia.org/wiki/Standard_deviation standard deviation], which is a measure of dispersion, and which is a parameter for the [http://en.wikipedia.org/wiki/Normal_distribution normal distribution]. | ||

− | [[File:Bivariate.png|400px|thumb|right|Distribution of samples from a bivariate | + | [[File:Bivariate.png|400px|thumb|right|Distribution of samples from a symmetric bivariate normal distribution. Axis units are multiples of σ.]] |

The [[Closed_Form_Precision#Symmetric_Bivariate_Normal_.3D_Rayleigh_Distribution|most convenient statistical model]] for shooting precision uses a bivariate [http://en.wikipedia.org/wiki/Normal_distribution normal distribution] to characterize the point of impact of shots on a target. In this model the same ''σ'' that characterizes the dispersion along each axis is also the parameter for the [http://en.wikipedia.org/wiki/Rayleigh_distribution Rayleigh distribution], which describes how far we expect shots to fall from the center of impact on a target. | The [[Closed_Form_Precision#Symmetric_Bivariate_Normal_.3D_Rayleigh_Distribution|most convenient statistical model]] for shooting precision uses a bivariate [http://en.wikipedia.org/wiki/Normal_distribution normal distribution] to characterize the point of impact of shots on a target. In this model the same ''σ'' that characterizes the dispersion along each axis is also the parameter for the [http://en.wikipedia.org/wiki/Rayleigh_distribution Rayleigh distribution], which describes how far we expect shots to fall from the center of impact on a target. | ||

## Revision as of 20:20, 24 May 2014

## What is sigma (*σ*) and what does it mean?

*σ* ("sigma") is a single number that characterizes precision. In statistics *σ* represents standard deviation, which is a measure of dispersion, and which is a parameter for the normal distribution.

The most convenient statistical model for shooting precision uses a bivariate normal distribution to characterize the point of impact of shots on a target. In this model the same *σ* that characterizes the dispersion along each axis is also the parameter for the Rayleigh distribution, which describes how far we expect shots to fall from the center of impact on a target.

Shooting precision is described using angular units, so typical values of *σ* are things like 0.1mil or 0.5MOA.

With respect to shooting precision the meaning of *σ* has an analog to the "68-95-99.7 rule" for standard deviation: The 39-86-99 rule. I.e., we expect 39% of shots to fall within 1*σ* of center, 86% within 2*σ*, and 99% within 3*σ*. Other common values are listed in the following table:

Name | Multiple of σ |
Shots Covered |
---|---|---|

1 | 39% | |

CEP | 1.18 | 50% |

MR | 1.25 | 54% |

2 | 86% | |

3 | 99% |

So, for example, if *σ*=0.5MOA then 99% of shots should stay within a circle of radius 3*σ*=1.5MOA.

*σ* also tells us what to expect from other precision measures. For example, on average a five-shot group has an extreme spread of 3*σ*. So if *σ*=0.5SMOA and we are shooting at a 100-yard target we would expect the extreme spread of an average 5-shot group to be 1.5".