Well, let me run you through how I do it when I need to calculate this kind of thing (thank the Omnissiah for it being almost universally roll 2, pick the highest)
Open up your trusty spreadsheet program and type out on the side 1,2,3,4,5,6 on lines 2-7 in column A, then along B-G type in (once again) 1-6.
In B2-B7 fill it with the highest (granting 1, 2, 3, 4, 5, and 6), then in C2-C7 do the same (granting 2, 2, 3, 4, 5, 6) and so on. Then just count and take it as a fraction of 36. Since we're going highest with this I'll just give you the fractions (N A/36, where N is the number you want the roll to be and A is how many times that or something higher shows up)
1 36/36
2 35/36
3 32/36
4 27/36
5 20/36
6 11/36
Edit: Oh, darn, the average... Okay well time to multiply and sum...
4.4722.... Simply put, all I did was multiply by the number of appearances of each number, sum, and then divide by 36.... so yeah ~_~ And, yes, his way is better, but I never got into solid probability based math and modeling equations, I'm more into solving them, finding limits, diff eqs, etc. Kind of stupid not taking Stats courses now that I think about it...