When Central Limit Theorem breaks down
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Let say I have following numbers 4,3,5,6,5,3,4,2,5,4,3,6,5 I sample some of them, say, 5 of them, and calculate sum of 5 samples. Then I repeat that over and over to get many sums, and I plot the values of sums in histogram, which will be Gaussian as Central Limit Theorem. But when they are following numbers, I just replaced 4 with some big number, 4,3,5,6,5,3,10000000,2,5,4,3,6,5 Sampling sum of 5 samples from these never becomes Gaussian in histogram, but more like a split and becomes two Gaussians. Is there any paper or research that mentioned this? Thank you
central-limit-theorem
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