The Central Limit Theorem Visualized with D3 • Hacker News Board

nphrk wrote: post #10

Jabbles wrote: post #5

This isn't the central limit theorem. This is a binomial distribution. Nice animation though.

It is the distribution of the average of n binomial distributions (taking on values x±1)†, which according to the CLT converges to a Gaussian as n→∞. [†] x is where it is centered.

n = 4.

Re: The Central Limit Theorem Visualized with D3

#16

Post by Jabbles » Thu, May 30, 2013, 9:03 PM UTC

[deleted] wrote: post #14

Jabbles wrote: post #5

This isn't the central limit theorem. This is a binomial distribution. Nice animation though.

[deleted]

Well, not really. The fact that CLT applies to a wide variety of distributions is a much stronger, mysterious and astonishing fact than what is demonstrated here.

It would be like demonstrating that you've cracked RSA with p = 7, q = 11.

Re: The Central Limit Theorem Visualized with D3

#17

Post by yid » Thu, May 30, 2013, 9:05 PM UTC

hanzq wrote: post #12

Here's a galton box. ( http://www.youtube.com/watch?v=AUSKTk9ENzg ) It's a meatspace demonstration of the CLT.

This was one of the most "a-ha moment" videos I ever watched back in the day. Anyone with even a functional knowledge of statistics should watch this one.

Re: The Central Limit Theorem Visualized with D3

#18

Post by calinet6 » Thu, May 30, 2013, 9:06 PM UTC

A great example of convergence in the natural world I once saw was drops of water falling off a gutter from about 10 feet in the air. There was very little wind, and the drops fell on a line right under the gutter. It was immediately clear that the drops landed in a roughly normal distribution with their random fall through the air, and the pattern of wet pavement they produced was a perfect little compressed bell curve. It was quite beautiful.

Re: The Central Limit Theorem Visualized with D3

#19

Post by calinet6 » Thu, May 30, 2013, 9:08 PM UTC

Jabbles wrote: post #16

[deleted] wrote: post #14

Earlier quoted context omitted.

[deleted]

Well, not really. The fact that CLT applies to a wide variety of distributions is a much stronger, mysterious and astonishing fact than what is demonstrated here. It would be like demonstrating that you've cracked RSA with p = 7, q = 11.

Agreed, learned more, was wrong, deleted comment. Curious though—doesn't the CLT apply to this distribution too, technically? Isn't the binomial distribution being sampled and converging on a normal distribution, as per the CLT? Maybe some more explanation would enlighten us.

Re: The Central Limit Theorem Visualized with D3

#20

Post by bcgraham » Thu, May 30, 2013, 9:08 PM UTC

Jabbles wrote: post #5

This isn't the central limit theorem. This is a binomial distribution. Nice animation though.

Well, to be accurate, it's four binomial distributions, not just one. You need the sum of ~30 random variables before you're getting into the CLT, but it demonstrates the gist.