The variance is denoted by [itex]σ^{2}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

It is calculated with this equation:

[itex]σ^{2}=\frac{\sum^{N}_{i=1}(Xi-μ)^{2}}{N}[/itex]

Which makes sense. To calculate the average (deviation from the mean)^2 you need to sum up the (deviations from the mean)^2 and then divided by the number of deviations.

The reason that you use (deviation from the mean)^2 instead of just the deviation from the mean is so that positive and negative numbers do not cancel out.

However in my lecture slides the formula is given by:

[itex]σ^{2}=\sum^{N}_{i=1}(Xi-μ)^{2}P(Xi)[/itex]

Which is different from what I have previously learnt.

All I can presume is that [itex]\sum^{N}_{i=1} P(Xi) = \frac{1}{N}[/itex]

But why? What is P(Xi), and why is it used instead of just using N?

On the previous slide there is an equation for P(X) which I presume is something to do with it.

This equation is:

[itex]P(X)=\frac{1}{σ\sqrt{2∏}} *e^{-\frac{(x-μ)^2}{2σ^2}}[/itex]

https://en.wikipedia.org/wiki/Normal_distribution

Although this doesn't make sense anymore. I used to be able to understand standard deviation and variance as the equations were quite intuitive, but now it makes no sense at all.

It would probably help if I understood the normal distribution (Gaussian Distribution) equation. What does this equation mean? And why is it used in the calculation of variance?

Please help!!

Thank you!!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Variations of the Variance Formula

Loading...

Similar Threads - Variations Variance Formula | Date |
---|---|

I One-Way Analysis of Variance | Dec 9, 2017 |

Correlation limits for binary variates | Feb 22, 2016 |

Find Function/Transform for signal that minimizes CV of data | Jul 19, 2015 |

Is this a variation on a residual plot? | May 4, 2014 |

Wasted random variates? | May 4, 2014 |

**Physics Forums - The Fusion of Science and Community**