The mean is given as a composition or amount vector of the same class as the original dataset.
Details
The different compositional approaches acomp,
rcomp,
aplus, rplus correpond to different
geometries. The mean is calculated in the respective canonical
geometry by applying a canonical transform (see cdt), taking ordinary
mean.col and backtransforming.
The Aitchison geometries imply that mean.acomp and mean.aplus are
geometric means, the first one closed. The real geometry implies that
mean.rcomp and mean.rplus are arithmetic means, the first
one resulting in a closed composition.
In all cases the mean is again an object of the same class.