Why is it not correct to average an average?

Answer 1

It may or may not be correct, depending on the situation. Here are two examples: let's say the average temperature for a given month, in a given city, is known. There is nothing wrong with taking the averages for all the other months (with one caveat), and thus finding the average for the entire year. (The caveat is, the averages must all be based on the same period of time, for example, if one month's average was computed over the last 50 years and another month for the last 80 years, then it is not valid to lump them together, as the data sources are different.) An example where it's not valid to "average an average." Say a Baseball player has been playing in the major leagues and you know his batting average for each year in his career. It would not be valid to take the averages for each year and add them together and divide them by the number of years played. This kind of "average of an average" is not valid because the player undoubtedly batted a different number of times each year. In other words, if he batted .300 with 100 at bats in one year, and .200 with 500 at bats another year, his career average is NOT .250, since the number of at bats was not taken into account.