I love numbers. When someone or a company has a rich set of data that’s meaningful, I like to really dive in. And so I am sometimes disappointed when the only figures that are presented are “averages.” Usually that translates into people presenting or writing about an arithmetic mean. But I often crave more, as an average figure tells you nothing about the distribution of the dataset.
Wikipedia explains further,
“[Mean] is used for many purposes and may be abused by using it to describe skewed distributions, with highly misleading results. A classic example is average income. The arithmetic mean may be used to imply that most people’s incomes are higher than is in fact the case. When presented with an “average” one may be led to believe that most people’s incomes are near this number. This “average” (arithmetic mean) income is higher than most people’s incomes, because high income outliers skew the result higher (in contrast, the median income “resists” such skew). However, this “average” says nothing about the number of people near the median income (nor does it say anything about the modal income that most people are near). Nevertheless, because one might carelessly relate “average” and “most people” one might incorrectly assume that most people’s incomes would be higher (nearer this inflated “average”) than they are.”
Examples like the one cited above are just the beginning. I often see statistics quoted in the popular media using “averages” which are incomplete at best, and misleading at worst. To me, averages are like snapshots as compared to a whole movie; they reveal a moment in time, but they don’t tell the whole story.