Naked Statistics: Stripping the Dread from the Data

by Charles Wheelan

The mean, or average, turns out to have some problems in that regard, namely, that it is prone to distortion by “outliers,” which are observations that lie farther from the center. To get your mind around this concept, imagine that ten guys are sitting on bar stools in a middle-class drinking establishment in Seattle; each of these guys earns $35,000 a year, which makes the mean annual income for the group $35,000. Bill Gates walks into the bar with a talking parrot perched on his shoulder. (The parrot has nothing to do with the example, but it kind of spices things up.) Let’s assume for the sake of the example that Bill Gates has an annual income of $1 billion. When Bill sits down on the eleventh bar stool, the mean annual income for the bar patrons rises to about $91 million. Obviously none of the original ten drinkers is any richer (though it might be reasonable to expect Bill Gates to buy a round or two). If I were to describe the patrons of this bar as having an average annual income of $91 million, the statement would be both statistically correct and grossly misleading. This isn’t a bar where multimillionaires hang out; it’s a bar where a bunch of guys with relatively low incomes happen to be sitting next to Bill Gates and his talking parrot.