The plot to the left shows the distribution of heights of American women, ages 20 to 29, according to the 2007/2008 census. Data here. I couldn’t find data on UK heights, but it should be similar. Data for the heights of men are similar but shifted up a bit. The circles are the data and the line is fit of a Gaussian function to this data. The most probable heights are around 165 to 170 cm (5 ft 4 in to 5 ft 6 in). The width (standard deviation) of the Gaussian fit is 7 cm.

The data is not perfectly fit by a Gaussian by any means, but the Gaussian shape is roughly right in the sense that the distribution is roughly symmetric about the peak and the peak itself is quite flat. The Gaussian fit is consistent with the height being the result of a sum of many small contributions, i.e., height is not determined by one or a few genes, each of which has a big effect on our height but by many genes each of which just shifts our height by a centimetre up or down. The Central Limit Theorem of statistics tells us that if a property is a sum of many small terms, each of which can be a bit bigger or smaller, then the distribution of the property should be a Gaussian.

I like results like this, where with a simple statistical argument, you can infer things about how our bodies are built. Animals such as ourselves are very complex things, and usually this complexity is a real pain, as it makes it very hard to understand what is going on. But here the very fact that apparently so many genes affect our height actually simplifies our task of finding the best model.

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