> the distribution of their sum Exactly. But the page defines the CLT as referring to: "the mean of a sufficiently large number of independent random variable

> the distribution of their sum Exactly. But the page defines the CLT as referring to: "the mean of a sufficiently large number of independent random variables ..." So it talks about the mean and then illustrates the sum, just as you are, which is confusing. I spent several minutes puzzling about how the mean of variables between zero and 1 could be 5, for example. Now, I suppose you will say, the distribution of the mean is just the distribution of the sum, normalized, and this ought to be obvious to anybody with half a brain, but if this page is meant to help people trying to learn this stuff understand it, it would be better if it was accurate and not directly confusing with its language.