You can't average people. Voters are not mathematical figures. The parties are, by their nature, coalitions of interest groups. There's no way to average a poor ghetto black person with a union member with an idealistic college kid to make an average Democrat. Similarly, you can't average a rural evangelical with a business minded country clubber with pro-war veteran to make an average Republican.
You can average anything out. You can mix the positions of all these people and come out with an "average" democrat or republican. Now whether that is a typical democrat or republican is a different question.. which in that case, for a typical voter of a certain party, you would take the position that agrees with the most people in the party, issue by issue... which is like finding the median... which is probably better and more accurate.. in teh same way that using median income is a more accurate picture of what a typical person earns in income as compared to the mean which gives weight to Mr. and Mrs. Hooty tooty up top earning 1000 times more than you and skewing the statistics.