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
- Mean far above median. Which direction does that put the tail?
- 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.
Practise Data Distributions and Skewness
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