Aside from population-wide sums or “averages” (in the specific sense of “arithmetic mean”), there's also models, medians, various distributional measures, etc. Which subset (which may include more than one selection) of these are most appropriate for a particular comparison depends on the specific purpose of the comparison. Arithmetic mean and/or sums are usually the easiest measures, but quite often not the most relevant.

I know, I'm trying to understand what studies contradict PISA and why is it faulty.