Is the mean always greater than the median in a right skewed distribution?

by Karen Grace-Martin

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One of the basic tenets of statistics that every student learns in about the second week of intro stats is that in a skewed distribution, the mean is closer to the tail in a skewed distribution.

So in a right skewed distribution (the tail points right on the number line), the mean is higher than the median.

It’s a rule that makes sense, and I have to admit, I never questioned it.

But a great article in the Journal of Statistical Education shows that it really only holds in idealized, unimodal, continuous distributions:  http://www.amstat.org/publications/jse/v13n2/vonhippel.html.

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