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If I have a mean of 15 and median of 10, is there a term for the difference between these?

Can you use this difference of 5 for anything valuable statistically?

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  • $\begingroup$ Tell us also the standard deviation and the interquartile range (IQR). $\endgroup$
    – smci
    Mar 5 at 7:29

1 Answer 1

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The ratio (mean $-$ median) / SD has often been used as a measure of skewness. It has the perhaps surprising feature that it is bounded by $-1$ and $1$. But I would never recommend using it by itself -- without checking other measures of skewness -- or without looking at some graphs of a distribution.

In your case, and generally, it is also important to know whether your variable is always positive or always zero or positive.

Section 7 of this paper carries a miniature review of skewness measures.

I don't recollect (mean $-$ median) ever being given a specific name. It doesn't need one.

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  • $\begingroup$ So $5$ is a lower bound on the standard deviation here. Incidentally, if you have a continuous unimodal distribution then (mean − median) / SD is bounded by $\pm \sqrt{\frac35}$ which would lead to a lower bound on the standard deviation here of $6.45$ $\endgroup$
    – Henry
    Mar 4 at 1:52
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    $\begingroup$ This is in Wikipedia as en.m.wikipedia.org/wiki/Nonparametric_skew $\endgroup$
    – Matt F.
    Mar 4 at 2:05
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    $\begingroup$ Pearson's second skewness coefficient is a multiple of 3 of this nonparametric skew. $\endgroup$
    – Galen
    Mar 4 at 2:13
  • $\begingroup$ Please see the linked paper and its references for much more detail. $\endgroup$
    – Nick Cox
    Mar 6 at 8:33

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