Actually there is a way to calculate the rigorous average every time a new frame is exposed:

Suppose 2 frames A1 & A2, then average = (A1+A2)/2

If you have 3 frames A1, A2 & A3, you can either do average = (A1 + A2 + A3)/3 or 2*(**(A1+A2)/2)**)/3 + A3/3.

Note that the part of the equation highlighted in bold is the same as the average of two images, or "Previous average", so we can write:

Average of n images = (n-1)*(previous average)/n + (new exposure)/n ; for the nth exposure.