I wasn't aiming to answer Locaha's question as much as figure out what question to answer. The range of math knowledge here is high, and I don't know where Locaha stands. I mean,

But why [is the mean calculated as] sum/n?

That could be a basic question about the meaning of averages -- the sort of knowledge I internalized so deeply that I have trouble forming it into words.

But maybe Locaha's asking a question like:

Why is an unbiased estimator of population mean a sum/n, but an unbiased estimator of population variance a sum/(n-1)?

That's a less philosophical question. So if Locaha says "means are like the centers of mass! I never understood that intuition until now!", I'll have a different follow up than if Locaha says "Yes, captain obvious, of course means are like centers of mass. I'm asking about XYZ".