I just averaged the last 5 national polls

[forgotmylogin]

6. Just to verify...you didn't compute an average of percentages, did you?

Poll A: 90 percent of respondents favor position X. 10 percent favor position Y.
Poll B: 40 percent of respondents favor position X. 60 percent favor position y.

90+40=130. /2 = 65% favor position X
10+60=70. /2 = 35% favor position Y.

The conclusion would seem to be people favor position X 65%-35%.

That's not how math works with percentages.
Percentages idealize the entire sample they are based on, and a percent of a larger group has more "weight".

If poll A had 10 respondents, 9 of them make 90%. 1 makes 10%.
If poll B had 1000 respondents, 400 of them make 40%. 600 of them make 60%.

If we combine them into one group of 1010 respondents:

409 favor position X. 601 favor position Y. (X and Y each /1010)%
40.5% favor position X. 59.5 favor position Y.

I once had to explain this slowly and in great detail to a person who made a whole lot more money than I do.