“Average” considered harmful

The vast majority of people have more than the average number of legs.

The average mother has 2.36 children even though no mother has that number.

We have an intuitive grasp of what it means when something is average, typical, or representative.  Math and statistics formalize “average” in terms of mean, median, and mode.  Each of these quantities condenses the complicated details of a distribution into a single number.

That number oversimplifies things, though.  Bizarre, counterintuitive, and seemingly paradoxical things happen with unusual (not-so-representative) distributions.

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