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Vaniver comments on How valuable is it to learn math deeply? - Less Wrong
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The example I'd give here is India, where you have lots of mostly distinct ethnic groups, and so it's reasonable to expect that the true distribution is a mixture of Gaussians. Knowing the Indian average national IQ would totally mislead you on the number of Parsis with IQs of 120 or above, if all you knew about Parsis was that they lived in India.
(It's not clear to me that malnourishment leads to multiple modes, rather than just decreasing the mean while probably increasing the variance, because I think damage due to malnourishment is linear, and it's probably the case that many different levels of severity of malnourishment are roughly equally well represented.)
In the limit, the mixture of Gaussians is a Gaussian.
Theoretically, malnourishment (given that only a part of the population suffers from it) should lead to a negatively skewed distribution. And yes, with a lower mean and higher variance.
Nope. The sum of Gaussian random variables is a Gaussian random variable, but a mixture Gaussian model is a very different thing. (In particular, mixture Gaussians are useful for modeling because their components are easy to deal with, but if you have infinite mixtures you can faithfully represent an arbitrary distribution.)
Yep, I should have mentioned that also.
Yes, you are correct, I got confused between a sum and a mixture.
Not everyone's malnourished, though - a significant number of people are into diminishing returns, nutrition wise. It's very nonlinear in the sense that as long as there's adequate nutrition, it plate-outs - access to more nutrition does not improve anything.