Can the mean of some sample of random variables be itself a random variable?

Yes?

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#### Best Answer

The mean of a collection of random variables is itself a random variable.

So if you have say, $X_1,X_2,X_3,…,X_n$, then $bar{X}=frac{1}{n}(X_1+X_2+X_3+…+X_n)$ is a random variable.

If you're talking about a sample of particular observations, $x_1, x_2, …, x_n$, then you could look at the sample mean, $bar{x}$ as another kind of observation, relating to the random variable $bar{X}$ in the same way that the observation $x_1$ relates to the random variable $X_1$, which is to say it's a realization of the random variable $bar{X}$.

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