> 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/central-limit-theorem.md).

# Central Limit Theorem

{% hint style="success" %}
It states that the average of the sample means will be equal to the population mean.
{% endhint %}

Irrespective of how the population data points are distributed, the plot of sample means will always look like a normal distribution. 

**For a normal distribution, we know that,**

* Mean, Median and Mode are equal 
* Data is symmetric about the mean 

Using these properties we can draw inferences about the population as a whole.