Simple set {3, 9, 2, 5, 7, 8}
Sum = 34, n = 6, mean = 34 / 6 ≈ 5.667. Median is 6. They almost agree.
Skew {10, 12, 11, 13, 1000}
Mean = 209.2, median = 12. If you need a typical household, quote the median. If you need total divided by headcount (budget per person including the outlier), the mean is the right identity.
Two speeds (harmonic)
Go 60 km at 20 km/h and 60 km at 60 km/h. Harmonic mean of 20 and 60 is 30 km/h — the actual average speed. The arithmetic mean 40 km/h is too optimistic.
FAQ
Why geometric mean missing?
It is hidden when any value is ≤ 0, because log is undefined.
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