But what is the Central Limit Theorem?
3,391,365
Published 2023-03-14
Help fund future projects: www.patreon.com/3blue1brown
Special thanks to these lovely supporters: www.3blue1brown.com/lessons/clt#thanks
An equally valuable form of support is to simply share the videos.
Galton board shown in the video: 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:
www.3blue1brown.com/faq#manim
github.com/3b1b/manim
github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
github.com/3b1b/videos/
Music by Vincent Rubinetti.
www.vincentrubinetti.com/
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/album/the-music-of-3bl…
Stream the music on Spotify:
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: 3b1b.co/subscribe
Various social media stuffs:
Website: www.3blue1brown.com/
Twitter: twitter.com/3blue1brown
Reddit: www.reddit.com/r/3blue1brown
Instagram: www.instagram.com/3blue1brown
Patreon: patreon.com/3blue1brown
Facebook: www.facebook.com/3blue1brown
All Comments (21)
-
Please consider doing an entire series on probability theory and/or combinatorics.
-
Hooray! A new 3Blue1Brown video!
-
I'm an engineering professor far more older than you and I must say whitout a doubt: you are the most skilled professor I have ever seen. The amount of work in this videos is outstandig. They are so flawless that can be considered as art. Congratulations!.
-
the section unpacking the Gaussian formula is simply a work of art. Giving a graphical intuition about moving from e^(-x) to e^(-x^2), and then to a constant multiplier of the exponent... just absolutely pristine
-
Of all the years I've supported 3b1b, this video might be the one I was most excited to see pop up.
-
Next video, explaining the π and how the function e^(-x^2) arises: https://youtu.be/cy8r7WSuT1I As many helpful commenters have pointed out, at 6:37 and 7:15 the narration should say "skews left" instead of "right". In standard terminology, the skew direction refers to the direction of the longer tail.
-
I have a PhD in applied mathematics, I work in numerical weather prediction as a research scientist. Gaussianity is this hardcore part of the basics of forecasting the weather (even though most atmospheric variables, and their errors, are actually non-Gaussian). This video did a great job at teaching the CLT. I have never seen it explained so well.
-
This series of lectures must be incorporated into the math curriculum of all high schools in the world, I was trained in math and as a data scientist, but I have never seen the central limit theorem explained this way. It just made things so easy to understand and intuitive. Well done.
-
Dealing with CLT pretty much every day here. Really impressed with how easily you explain it. By far the most intuitive and easily understood explanation of CLT. Salute!
-
The actual rigorous no-jokes-this-time conclusion from watching 3Blue1Brown videos like this is that Grant deserves some new, yet-to-be invented prize that should be the equivalent of an Oscar for best computer generated imagery, an Emmy for outstanding narration / editing and a Nobel Prize in science for fostering interest in mathematics and science. Amazing, inspired work here.
-
Retired aerospace engineer here. Eons ago I was working on a new aircraft project where parts for the aircraft had to be certified for a particular random vibration environment, 6-sigma to be exact. Vibration shakers were used to test the parts. The shakers had to be limited to 3-sigma to prevent damage to the shakers. So the concern was that the responses of the parts weren't exposed to the full Gaussian spectrum and thus limited to 3-sigma. I used similar analysis described in this video to show that the part was indeed being tested appropriately. Too bad this video wasn't around back then.
-
I can't tell you how insanely brilliant you are at taking a universal concept that is vaguely understood and illuminating all the nuance hidden in plain daylight to make this understood on a higher level!!! Genius
-
Grant, you are a lifesafer! My exams are in 2 weeks and I have not understood this yet. It's a miracle you are publishing this video online!
-
As someone who works with Kalman filtering on a regular basis, this is a very nice video to see. One of the core principles behind the Kalman filter is that all random variables involved must be Gaussian, which seems overly restrictive on the surface. I think this provides an excellent, succinct explanation for why that's actually a reasonable assumption for many systems, since every random process we can directly observe is really just a combination of many smaller processes. I look forward to the next one!
-
If there is a Fields Medal for Math Content creators on Youtube it should be for this channel. Grant Sanderson, you are awesome sir.
-
Thanks for producing such high-quality videos, i'm a maths student who love statistics. I would say this vid gives the clearest and neatest explanation to CLT ever, really inspiring, I sacrificed my sleep time watching it for 3 times!!! Amazed and shocked! Thank you Grant. <3
-
You know, I really like math, so I went to a natural science uni to study it. I spent 3 years there, but it was a dry way of learning math and eventually I dropped out. Watching this video (and your videos in general) I understand so much more about probability than what they could have ever thought me.
-
I would absolutely love to see a series on probability/combinatorics/statistics on this channel. It's the subject I've struggled the most with in math by far. I think your ability to take the time to really think through and understand what the basic building blocks really mean will become a very valuable resource in my and many other people's math journeys.
-
Describing the mean of the weights as the center of mass of the distribution was just incredible. And the intuitive matrix multiplication without even mentioning it. You are a great teacher!
-
I am constantly impressed by how Grant's videos extract the art that is inherent in certain mathematical concepts. What a great video!