I'm familiar with this way of doing an arithmetic mean in J:
+/ % #
But it's also shown here as
# %~ +/
Are these two versions interchangeable, and if not when should I use one versus the other?
Dyadic ~ reverses the arguments of a verb. x f~ y is equivalent to y f x. You use ~ when you, um, want to reverse the arguments of a verb.
One of its most common uses is for forks and hooks composition. For example, because y f (g y) is (f g) y you can use ((f~) g) y when you need (g y) f y.