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by joker3
2366 days ago
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1) Human height isn't actually bimodal even if some histograms display two modes. See https://amstat.tandfonline.com/doi/abs/10.1198/00031300265#.... for an analysis. 2) The central limit theorem applies to the distribution of the sample average. It applies whenever the samples are iid and the second moment is finite. The fact that the samples are coming from a mixture of normals doesn't change that. |
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"Bimodal" doesn't really have a precise definition or test, if you don't assume normal distrubtions.
That paper argues that only if means are separated by 2σ should the distribution be considered bimodal.
But there are many measures of bimodality. [1] [2] [3] [4] [5] [6]
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In any case, I would be very much surprised if the population couldn't be selected enough (age, race, country, diet, family) to have human height be bimodal by any measure.
[1] https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/97WR...
[2] https://journals.sagepub.com/doi/10.4137/CIN.S2846
[3] https://link.springer.com/article/10.1007%2Fs11207-008-9170-...
[4] https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1469-1809....
[5] https://link.springer.com/article/10.3758%2FBF03205709
[6] https://esj-journals.onlinelibrary.wiley.com/doi/abs/10.1007...