Hi

So this might sound like a trivial questions Is it possible to calculate the average genome size in a mixed dataset composed of complete (closed) genomes and assemblies?

As biostars say - No question is too trivial or too "newbie".

I assume that you are taking about metagenomic samples. The answer is no. See why

Average genome size usually means a wise estimation of the genome size of species or a consensus of the genome size of different strains of same organisms. For example, different bacterial strains (same at species level) may have varying genome size. Same is true for bacteriophages which have a broad range of genome size. So generally, it is referred that a xyz organism's genome size range from say, for e.g. 100-150 mb. That is the average size.

I've seen it in some papers, where they report average genome sizes of complete and draft genomes, but can't quite figure out how they do it (or if it is correct) Is there a particular definition of average genome size?

It's usually done by 2 ways- through wetlab techniques like flow cytometry and via computational methods like kmer analysis. See this paper