Like the title says, does $X$ (a random variable) usually refer to the population or the sample?
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1$\begingroup$ Have you read the answers at stats.stackexchange.com/questions/50? $\endgroup$ – whuber♦ Sep 24 '15 at 14:10
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I think the question is ill-posed.
A random variable, by definition, is a misurable function. If you estract a sample from a population, they follow the same distribution, so the random variable can describe both. When you use the term "Random Variable" you refer to a function from a set to another, the first being called "sample space" and the second $\mathbb{R}^n$.
I could write you the proper definition, but I don't think that would help in this case, moreover you can find it everywhere (starting from Wikipedia).
