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

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://jse.amstat.org/v13n2/vonhippel.html.

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  1. Nory says

    It says that it is skewed to the right when the mode is less than the median and the mean. My data is unique in this case since the mode is less than the median and the mean but the mean is less than the median. I decided that the data is skewed to the right. I hope I’m right. Please give your feedback. Thanks!

  2. Sparsh says

    True. I found some instances where it wasn’t true, although there was only slight difference in mean and median.


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