Meaning of Field methods mean(), var() and std() is unclear

Are we sure that the Field reduction methods mean(), var() and std() are doing what we expect from them?

Currently, mean() computes a straightforward average over all entries, without taking volume factors into account. Is this what we want? For GLSpaces, the result may not be the desired one.

@theos, @kjako, @dpumpe, @reimar: what are the official/intended semantics?