So I've done the algebra for this little equation about 6 times in the last year, so I figured I'd put it here so I won't have to do it again, and so anyone else in the world can get it, since I haven't been able to find it online.

Suppose you need to calculate an average value; but it's the average of A LOT of values, so many that you can't just add them all up and divide because round-off errors will hurt if you keep multiplying up a huge number every time. You can keep a running average. One benefit is that you have the average of all values so far seen at every step of the way, and you never need to calculate a really big number, you do have to keep track of the number of values already entered, but that's simple enough:

new_ave = cur_ave - (cur_ave / num_vals) + (new_val / num_vals)
-- where num_vals = the number of values input including the new_val

Example:
For values 1, 3, 8, 4
0 - (0/1) + (1/1) = 1
1 - (1/2) + (3/2) = 2
2 - (2/3) + (8/3) = 4
4 - (4/4) + (4/4) = 4

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