# Notation for Average of a Set?

In particular, I have some set $S = \{s_1, s_2, s_3, ..., s_n\}$ and a subset $S^\prime$, and I want to denote the average of the elements in $S^\prime$. I would generally just use $\frac{\sum\limits_{i=1}^n s_i}{n}$, but $S^\prime$ only contains some of the elements of $S$ and so this won't work. This page suggests that the proper notation is $\left<S^\prime\right>$, but I wasn't able to find this anywhere else. Is this notation common, or is there some other accepted notation that I could use? Thanks!

(This is in a computer science paper, if it makes a difference.)

• it's a common notation in statistical mechanics and thermodynamics. – symplectomorphic Feb 27 '15 at 23:40
• I've always used $\overline{S}$ to denote the average of set $S$. – Conor O'Brien Feb 27 '15 at 23:42

Physicists may use $\langle S'\rangle$; statisticians might write $\bar{S'}$. But since you mention $\displaystyle\sum_{i=1}^n s_i /n$, I suggest $\displaystyle\sum_{s\in S}s/|S|$ or $\displaystyle\sum_{s\in S'}s/|S'|$, as the case may be. In some contexts one could write $\displaystyle\sum S/|S|$.