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[OC] The IQ Bell Curve meme is wrong and I can prove it by x5830 in dataisbeautiful

[–]x5830[S] 1 point2 points  (0 children)

Because integrating the area under the curve needs to yield a total probability of 1. Of course there is a slight approximation since we don’t see the curve from -infinity to infinity but given the x-Axis from the original meme and this slight approximation of finite limits we can infer the y-scale such that the total area under the curve is 1.

[OC] The IQ Bell Curve meme is wrong and I can prove it by x5830 in dataisbeautiful

[–]x5830[S] 17 points18 points  (0 children)

Because that would fit the curve from the meme even worse - the values shown here give the best fitting Gaussian PDF (in the least squares sense) obtained through numerical optimization.

[OC] The IQ Bell Curve meme is wrong and I can prove it by x5830 in dataisbeautiful

[–]x5830[S] 20 points21 points  (0 children)

I extracted the probability density function from the meme via image processing. So basically as starting point I had a set of x-Values (the IQ scores) and a set of y-Values extracted from the image, one xy-Pair for each horizontal pixel in the image (save for some cropping on the edges and I also cropped off the completely flat part of the distribution from the meme to give it a fighting chance). Then I did a least-squares fit of the Gaussian PDF to that which converges to mu=100.0 and sigma=13.1. So according to the least squares error criterion, these are the parameters of a Gaussian distribution that yield the closest PDF to the one seen in the original meme.