Like Thom, I was thinking when I made my post that total was the easy concept and average the difficult concept. But there are too many natural examples where people are talking about average, not total. When we say someone is usually happy, we are not making a claim about how many times we have seem them happy, but instead a claim about what percentage of the time they are happy. Faced with a collection of x's and o's, I think we are more inclined to think/perceive "There are a lot of x's" than to count the x's.
So then why would anyone have trouble with average? Maybe the formula is misleading -- the addition of numbers is most salient in the traditional formula. As Dennis remarks, dividing by n then "controls" for the number of numbers in the set. But how intuitive is that? So I was looking for a formula that did not involve addition. Maybe the first moment (terminology?) is the more natural formula? The first moment, if I have my terminology correct, is the number such that summation of each number minus the first moment is zero. That formula does not make addition salient -- the only addition is in the error term, and everything is supposed to cancel out to zero. Instead, that formula emphasizes a comparison of the average to every number, with the amount the average is greater (than a number in the set) balancing out the amount the average is less (than a number in a set). Well, that was more than I had planned to think about this! Thanks everyone for your responses. Bob . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
