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 Thanks to these viewers for their contributions to translations Hebrew: David Bar-On, Omer Tuchfeld Hindi: Tapender1 Italian: anna-lombardo ----------------- 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 Correction: 6:37 The narration should say "skewed left" Correction: 7:15 Again, the narration should say "skews a tiny bit left" ------------------ 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: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ 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