Sneaky averages

There's an old story about the statistician who drowned after seeing that the average depth was 3ft.

Averages, or in this case the mean, necessarily hide some data, but very often they also hide what's really going on.

• Say you run a delivery service and have an average delivery time of one day; it could be that most deliveries are actually a few hours, while just a few have people waiting for a week.
• A figure of average incomes might mask the fact that most people have low salaries, while a few are millionaires.
• My Dad, who did a lot of flying for work to conferences, to visit collaborators, used to joke about calculating your average height above sea level. If you spend most of your hours at 10 ft above sea level and just enough at 20,000 ft, then your average height has you floating tens or a few hundred feet in the air. This tells you very little about where the person is likely to be right now.

Just looking at the average for each of these, you can't tell much.

Sometimes a different measure of central tendency, like the median, can provide a clearer picture.

Sheldon Zedeck, a UC Berkeley psychology professor who taught me about the design of experiments, gave wise advice: "Spend time with your data."

Sometimes it's the only way to know what's happening for sure.