This seems a matter of preference to me. I personally always prefer to use \overline, as I find the \bar line to be very short (particularly if you have something wider than a single letter, like f_T). Apart from that preference, I'd point out two small differences between including the _T under the line, or not.
- If by the mean of
f_T, you mean: the mean of f, and afterwards specifying some T, I would suggest \overline{f}_T
- If
f_T is the actual function you are taking a mean of, I would suggest \overline{f_T}
By your description, I would suggest the second.
In general, if you are unsure, you can always make a command
\newcommand*\mean[1]{\overline{#1}}
and use \mean{f_T}, so you can change to \bar if you'd prefer that at a later point.
\mean{f_T}should not be stretch over_{T}? – Bernard Aug 14 '15 at 11:38