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Comment by thih9 | Hacker News Reader

Is all fun and games until one or two of the extreme remaining values (that are later used to replace the rest) turn out to be an outlier in itself.

Yes, but by definition they must strictly be less of an outlier than the values they are replacing.

Right but it can still pull the "Windsorized mean" to a particular direction. E.g. if your distribution is

    -99, 1, 1, 1, 1, 1, 2, 2, 2, 98, 99

and you "Windsorize" your mean, you'll pull it towards one direction.

Here, we get:

    mean: 9.91
    median: 1
    Windsorized mean: 18.91
    truncated (Olympic) mean: 12.11
    2-truncated mean[1]: 1.43

as you see "Windsorized mean" is exaggerated on the positive direction.

[1] this is when I remove top and bottom 2 values and calculate the mean of all the remaining values.

Windsorized (and trimmed) means really only work if you have one long tail, not two.

A Windsorized mean is when you replace the outliers with members of the British royal family.

Oh whoops sorry about the typo!