Psychology I / Data Distributions and Skewness
Practice question · Multiple choice

A charity reports that the mean donation to its campaign was £340. A journalist checks and finds the median donation was £25. Neither figure is wrong. What has almost certainly happened, and which number should the headline use?

Hints
  1. Mean far above median. Which direction does that put the tail?
  2. Ask what each figure is good for: describing a typical donor, or describing total income?
Show the answer

C. A few very large gifts have pulled the mean above the bulk.

Why

A mean thirteen times the median is the signature of a strong right skew, and donations have exactly the structure that produces one: a floor at zero, no ceiling, a handful of major gifts. Both figures have legitimate uses, median for the typical supporter, mean for what a donor is worth to the budget. The dishonest move is choosing by which sounds better and not saying which you used.

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