> For the complete documentation index, see [llms.txt](https://ai.nuhil.net/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://ai.nuhil.net/statistics/standard-deviation.md).

# Standard Deviation

{% hint style="success" %}
Standard Deviation is a measure of how spread out numbers are. 
{% endhint %}

It is the square root of the [Variance](/statistics/variance.md). It is often more convenient than the variance because it has the same unit as the data points.

**Population Standard Deviation**, $$\sigma=\sqrt{\frac{1}{n}}\sum\_i^n(x\_{i}-\mu)^2$$ 

**Sample Standard Deviation**, $$\sigma=\sqrt{\frac{1}{1-n}}\sum\_i^n(x\_{i}-\overline{x})^2$$