Let us suppose that I have some frequencies of experimental data on a plot, a histogram. The graph of such frequency data looks completely noisy. But I have a finch that if I could reorder the categories, it may appear as normal. I have many categories, of the order of 350, so the number of possible permutations is insane, and doesn't seem to be amenable to visual inspection. Is it possible to know in principle if the data would be Gaussian. By the way, I do not know if the categories have a natural ordering, at this moment they are just arbitrary labels, but if they were Gaussian in their frequencies, then I would know the order.
2026-03-25 06:05:18.1774418718
How to know that if by rearranging a histogram it would fit a Gaussian?
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If those categories are not related to a "hidden variable" that takes values in a monotonic sequence, this ordering does not make much sense.
You can sort the categories by decreasing frequency to see some regularity appear, but this ordering can be quite artificial and will vary from a dataset to another.
The distribution will not be Gaussian-like, but half-Gaussian-like. You can further split the histogram to make it symmetrical and Gaussian-like, but this will be even more arbitrary.