The mean average, roughly defined as the value all members of a set of things would have if they were all the same value, is a mathematical concept that is often useful, but also often overused. Maybe the most egregious example recently has been average wealth. As we've seen, the average wealth in the U.S., more properly known as the Gross Domestic Product (GDP) per capita, is something that tells you very little about how a typical American is doing financially these days. As we have seen, a small number of people can do very well, while everyone else sees no improvement, and the GDP per capita will still rise. For a better picture of how most of us are doing, looking at the median personal income is probably a better measure. That has changed little in the last couple of decades.
xkcd provides another example, a fictionalized one from the world of online product evaluations:
Image credit: xkcd
The trick to understanding the meaning of an average, of course, is to understand the set of data it's calculated from.
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