bar is generally used to denote means, but why because someone did it that way, presumably because it seemed like a good idea at the time, and then other people followed suit, as with almost any notational convention. m was often used for means of both distributions and of samples across a wide range of time; it's "re-invented" regularly. I always assumed the bar came from physics. The use of a bar over small x is discussed here: https://mathshistory.st-andrews.ac.uk/Miller/mathsym/stat/ (or see the older version of the page here http://www.math.hawaii.edu/~tom/history/stat.html ) ... scroll about 3/4 of the way down, to the section headed SYMBOLS IN STATISTICS and look at paragraph 2. It looks like it did indeed come from physics. Why are there competing conventions, anyways? Because people keep ignoring existing conventions in favor of ones they like for one reason or another (sometimes out of ignorance, sometimes with a pedagogical motive, sometimes to avoid a clash with some other convention, etc). Standards always multiply. Just recently (i.e. in the last few decades) it happened when ML people started adopting a lot of statistical methods and redefined all the terms and symbols (sometimes to match their own pre-existing terms, sometimes out of ignorance that there was already a good term/notation, sometimes for other reasons). Sadly, some of those conventions cause serious issues (like calling a regression coefficient a weight, leading to a serious clash when you need to talk about weighted regression). Answer from efrique on reddit.com

bar is generally used to denote means, but why because someone did it that way, presumably because it seemed like a good idea at the time, and then other people followed suit, as with almost any notational convention. m was often used for means of both distributions and of samples across a wide range of time; it's "re-invented" regularly. I always assumed the bar came from physics. The use of a bar over small x is discussed here: https://mathshistory.st-andrews.ac.uk/Miller/mathsym/stat/ (or see the older version of the page here http://www.math.hawaii.edu/~tom/history/stat.html ) ... scroll about 3/4 of the way down, to the section headed SYMBOLS IN STATISTICS and look at paragraph 2. It looks like it did indeed come from physics. Why are there competing conventions, anyways? Because people keep ignoring existing conventions in favor of ones they like for one reason or another (sometimes out of ignorance, sometimes with a pedagogical motive, sometimes to avoid a clash with some other convention, etc). Standards always multiply. Just recently (i.e. in the last few decades) it happened when ML people started adopting a lot of statistical methods and redefined all the terms and symbols (sometimes to match their own pre-existing terms, sometimes out of ignorance that there was already a good term/notation, sometimes for other reasons). Sadly, some of those conventions cause serious issues (like calling a regression coefficient a weight, leading to a serious clash when you need to talk about weighted regression). Answer from efrique on reddit.com