But what is the Central Limit Theorem?

A visual introduction to probability’s most important theorem
Help fund future projects: https://www.patreon.com/3blue1brown
Special thanks to these lovely supporters: https://www.3blue1brown.com/lessons/clt#thanks
An equally valuable form of support is to simply share the videos.

Galton board shown in the video: https://amzn.to/3ZJK8nY

—————–

Timestamps
0:00 – Introduction
1:53 – A simplified Galton Board
4:14 – The general idea
6:15 – Dice simulations
8:55 – The true distributions for sums
11:41 – Mean, variance, and standard deviation
15:54 – Unpacking the Gaussian formula
20:47 – The more elegant formulation
25:01 – A concrete example
27:10 – Sample means
28:10 – Underlying assumptions

——————

These animations are largely made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

You can find code for specific videos and projects here:
https://github.com/3b1b/videos/

Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/

Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:

——————

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown