Q:

Is there a notion of "multiplicative averaging"?

We can average $a,b\in \mathbb{R}$ by the simple calculation
$$\frac{a+b}{2}$$
The above is the usual average. Now, I wonder if a notion for "multiplicative average" exists, where we take ($a,b>0$)
$$\sqrt{a b}$$
Clearly, this is nothing like the actual average, but it seems to me that such an operation might be useful in a similar fashion as the average. Does it exist in some context? And if yes, how is it called properly?

A:

Yes, this is called a geometric mean. The average you already know is called an arithmetic mean.

