One thing I never realized until I started teaching is why we calculate the sum, then divide by the number of numbers to find mean. We're actually finding how much each person would get if the items were distributed equally. So if there were 3 apples, 5 apples, and 10 apples, if we combined them we would have 18 apples. Dividing by 3 gives 6 apples per person if the apples were shared equally. This also shows why we use median rather than mean for items like income where there can be outliers that skew the results when the items are shared equally.This reminds me of Ron Aharoni saying that when he taught arithmetic he realized there were subtleties to elementary mathematics that he hadn't thought about.
Must find that passage & post!
gasstationwithoutpumps on mean, median, & mode