> For the complete documentation index, see [llms.txt](https://docs.abi.am/abi-omicss-guide-2021/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.abi.am/abi-omicss-guide-2021/week-4/statistics-and-r/central-limit-theorem.md).

# Central Limit Theorem

## edX Course

Visit the [edX course](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/home), and complete the following:

1. [The Normal Distribution](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@0940279eeda74a5db377348992873755)
   * [Normal Distribution Exercises](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@e664f7059082463fa69c6ec64f310f9f)
2. [Populations, parameters, and sample estimates](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@74b2c3d1840f430db8017af8ceac0a62)
   * [Populations, Samples, Estimates exercises](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@df7325b3a65644a099270c95742ce62f)
3. [Central Limit Theorem (CLT)](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@6423da71519a492ab2f06387f9bf5aa7)
   * [Central Limit Theorem Exercises](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@14323fa8bd2246f78b0b51418d670ba8)
4. [CLT in Practice](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@e7d7c6baa85843fe9dc5e7518e691e5b)
5. [T-test](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@6f178bea3366401ab21d93c5d47162ea)
   * [T-test Exercises](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@997dd497b71c4232a588778f28cf894e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@dbafd787176f41cfabf50929f3792660)
6. [T-test in Practice](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@c5881a2f6d9047979b9c59d52ed65114)
   * [CLT and t-distribution in Practice Exercises](https://learning.edx.org/course/course-v1:HarvardX+PH525.1x+3T2020/block-v1:HarvardX+PH525.1x+3T2020+type@sequential+block@d27d8d24b8c443c3acb9e8ac2877f99e/block-v1:HarvardX+PH525.1x+3T2020+type@vertical+block@f2118c080c1f4db0984773dfb2061b0f)

## Alternative: Coursera Inferential Statistics

If you find the edX course too difficult or would like to read the same topic in alternative resources, consider [this Inferential Statistics course](https://www.coursera.org/learn/inferential-statistics-intro) offered by Duke University.

{% hint style="info" %}
Make sure to enroll in the course as before (Audit course option)
{% endhint %}

Watch the following videos:

1. [Introduction](https://www.coursera.org/learn/inferential-statistics-intro/lecture/EXe3o/introduction)
2. [Sampling Variability and CLT](https://www.coursera.org/learn/inferential-statistics-intro/lecture/lkQnZ/sampling-variability-and-clt)
3. [CLT (for the mean) examples](https://www.coursera.org/learn/inferential-statistics-intro/lecture/XhkI6/clt-for-the-mean-examples)

## Alternative: Statquest

For even more resources, check out the following videos on the topics of the normal distribution and the central limit theorem.

{% embed url="<https://www.youtube.com/watch?v=rzFX5NWojp0>" %}

{% embed url="<https://www.youtube.com/watch?v=YAlJCEDH2uY>" %}

## Congratulations!

If you made it here, then congratulations! You have successfully completed this section. Move to the next portion of the guide with the arrow buttons below.


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://docs.abi.am/abi-omicss-guide-2021/week-4/statistics-and-r/central-limit-theorem.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.