When computing the average of two numbers, yes, (a+b)/2 is the definition, but it's often a very suboptimal algorithm for *calculating* it in practice. Most of the time, you want a + (b-a)/2; numbers that get averaged tend to be close together so this requires less computation.
It boggles my mind that this is not taught in schools; I've seen so many people try to average, say, 467240 and 467285 by first computing 934525 and then dividing it back by two. DON'T DO THAT!!!!1!1!!
For three numbers, it's a + (b-a)/3 + (c-a)/3.

And while we're at it, for a geometric mean you can of course do a * sqrt(b/a), though this tends to be an optimization less often; inputs to geometric means seem to be more likely to be far apart.
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