The mean from a representative sample is, if you got the representation right, "equal" to the mean from a random sample, and both are "equal" to the population

The mean from a representative sample is, if you got the representation right, "equal" to the mean from a random sample, and both are "equal" to the population average. The problem with representative samples is that you can't know whether you've actually constructed one, and even if you have, you'll find it hard to compute the errors of your estimations. My beef is not with thinking of traditional frequentist-objectivist statistics as a set of algorithms solving specific problems (because that's what it is), my beef is with not starting out explaining exactly when the algorithms apply and why. When you take a black boxy algorithmic approach to something, you have to be particularly clear about things like that.