I'd like to know why in the weak low of large number we talk about empirical means (plural) $\overline{X}_n$ (I'm considering a series of $n$ random variables $X_i$). Are we using the plural because we can define a mean for each random variable or for other reasons?
If possible write the formulas of at least two means in order to understand the differences between them.
I guess we just use the plural to emphasize that we consider a sequence of means, indexed by $n$.