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This isn't the central limit theorem. This is a binomial distribution. Nice animation though.
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 museum exhibition:
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.
In the visualization as you increase the number of bins, the Gaussian approximation becomes more and more squeezed, and by the weak law of large numbers the limit is a Dirac delta.
In order to get the Gaussian you'd need to be looking at a window whose width is proportional to the square root of the number of bins.
while i have the attention of HN, does anyone have suggestions on any other types of statistic visualizations?
while i have the attention of HN, does anyone have suggestions on any other types of statistic visualizations?
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…
Earlier quoted context omitted.
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.
For instance, see: https://en.wikipedia.org/wiki/De_Moivre%E2%80%93Laplace_theo...
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…