Formatting: $\overline{X_1}$ or $\overline{X}_1$? To represent the means of a two random variables $X_1, X_2$, should the bar also cover the subscript, i.e.

should it be
$$\overline{X_1},\overline{X_2}$$
or
$$\overline{X}_1,\overline{X}_2$$

and why?
The first option seems to be the logical choice but the second option looks neater.

Addendum: If we decided that the first option is the appropriate one, what would the second option then represent?
 A: In this situation, the first option certainly seems more “logical,” i.e. you can interpret its meaning right away.
However, you can also justify the second by considering $X$ to be tuple of two random variables (with components $X_1$ and $X_2$) and the mean of the tuple to be the tuple $\overline{X}$ with components
$$
    \overline{X}_i = \overline{X_i}
$$
for every relevant index $i$ (i.e. $i \in \{1, 2\}$). This is what I would expect the second notation to denote – so the second would really be the same as the first.
After all, considering their visual similarity, it would almost seem malicious to use them for different things.
A: The notation $\overline{X_i}$ is more correct if you indicate $X_i=Y$ as a random variable.
Often you can find the notation $\overline{X}_n$ which means the sample average of the rv $X$ based on a $n$ size simple random sample.
This is taken from Mood Graybill Boes, McGraw Hill

In other words,
$$\overline{X_n}$$
indicates the sample mean of the rv $X_n$ but
$$\overline{X}_n$$
indicates the sample mean of the rv $X$ calculated on a $n$ sized random sample from $X$
A: $$\overline{X_n}=\frac1n\sum_{i=1}^nX_n$$ is the average of the samples $X_n$.
$$\overline X_n=\frac1m\sum_{i=1}^mX_{m,n}$$ is the average of the $n^{\text{}th}$ distribution.
In practice, both notations are probably used interchangeably (though illogically).
