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The Central Limit Theorem Visualized with D3

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Re: The Central Limit Theorem Visualized with D3

#31

Post by sp332 »

vicapow wrote: post #27
pseut wrote: post #22

Kind of a misleading animation, since n is the number of switches (4) and not the number of balls (which diverges to infinity). Setting the bins to 500 froze the browser, unfortunately. The physical machines that do this are undeniably cool, but especially when they have the curve painted on beforehand; this is the best I could find right now, but I remember seeing a pretty big one as part of a traveling mathematics…

what browser are you using? the bins tag has a max value set to 25

I'm using Firefox 22.0 and I have no problem setting it higher than that.

Re: The Central Limit Theorem Visualized with D3

#35

Post by dietrichepp »

baby wrote: post #32

I have to learn this Theorem for my exams (which are in a week). All I know is that (X1+X2+ ... + Xn - n * mean)/sqrt(n * variance) --> N(0,1) I don't see how that is visualization of this theorem.

X1, X2, ..., XN are Bernoulli(0.5) variables. You can increase N to show that the distribution approaches a Gaussian distribution, as long as you normalize the variance correctly (otherwise you get either no distribution at all, or you get a delta distribution).

Re: The Central Limit Theorem Visualized with D3

#36

Post by SiVal »

wtvanhest wrote: post #7
Jabbles wrote: post #5

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

Why isn't it the central limit theorem? It is taking random results and building a distribution which looks normal.

Imagine you have a population that is NOT normally distributed. Take a large sample of it, and calculate the mean of your sample. Then take another large sample of that population and calculate its mean. Keep doing this. Think of each sample mean as a data point that gives you an estimate of the mean of the whole population. The Central Limit Theorem says (approximately, and there are conditions) that those sample-mean data points of yours will be normally distributed, even though they were obtained by sampling a non-normal distribution. This also works when the population IS normally distributed, but that's not a surprise. The surprise is that the sample means are normally distributed even when the population isn't. (And again, there are some qualifications I'm not mentioning.)

So, sample means (estimates of the population mean) tend to be normally distributed even when the population they are sampling is not.

The D3 demo here doesn't show multiple sample means, it shows that as you take more and more items from a normal population, the distribution of your sample of items gradually comes to resemble the distribution of the population as a whole.

Re: The Central Limit Theorem Visualized with D3

#38

Post by dietrichepp »

calinet6 wrote: post #18

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 cu…

Well, it wasn't perfectly normal. But it was close. The Central Limit Theorem is about closeness, not perfection.

Re: The Central Limit Theorem Visualized with D3

#39

Post by dietrichepp »

coherentpony wrote: post #23

This is not the Central Limit Theorem.

Really? I see a collection X1, X2, ..., XN of Bernoulli(0.5) variables and the demonstration that the distribution of their sum, normalized for variance, approaches the Gaussian distribution as N increases. Is that not a direct consequence of the CLT?

Re: The Central Limit Theorem Visualized with D3

#40

Post by vicapow »

cypher543 wrote: post #29

You may want to do a bit of proofreading. It's difficult for me to take the content of this article seriously with so many spelling mistakes; especially since you misspelled "probability", which is the focus of the entire thing.

thanks for pointing this point. I updated the document.
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