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Which one is the "one true average" in {3, 5, 13}?

What about in {3, 4, 4, 5}?

The average number of legs per person is slightly less than 2. No person matches the average (and most of the world's population is above average).

Median - sure, though in an arbitrary sense since there could be other identical performances.

Mode - one number is average but there’s more than one identical number.

Mean - it’s possible that there’s more than one exactly average number.

Consider a standard curve where the mode mean and median are all the same… it’s quite common to have multiple ‘true averages’ lol

Came here to say this.

Not one sample must represent actual average. The average of 2 extremes will not be representative of either.

Same.