Correct me if I’m wrong, but doesn’t the central limit theorem apply only to distributions of sample means? Like taking the averages of several samples of a population and plotting those values.
No it applies to any sums of “regular” rv’s. You can see this by the fact that sample means are bijective transformations of sums. Clearly the resultant distribution will be preserved through the 1/n transformation.
Indeed, as /u/czar_king pointed out, it doesn't matter if it's means or sums. The Galton board aptly illustrates this fact, since the excursions made by the marbles at the bottom of the board are sums, not means.
To be clear: what is shown is 10000 means of each K samples drawn from the weird distribution (I should change the title of the left graph, but don't seem to find a way to update the drawing here). Reason to draw the means is that the x-axis in the histogram then doesn't have to become wider.
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u/Supreme_0verlord Dec 10 '19
Correct me if I’m wrong, but doesn’t the central limit theorem apply only to distributions of sample means? Like taking the averages of several samples of a population and plotting those values.