# Deviation between Mean and Median

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?

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

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.

• 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 $6.45$ Commented Mar 4 at 1:52
• This is in Wikipedia as en.m.wikipedia.org/wiki/Nonparametric_skew
– user225256
Commented Mar 4 at 2:05
• Pearson's second skewness coefficient is a multiple of 3 of this nonparametric skew. Commented Mar 4 at 2:13
• Please see the linked paper and its references for much more detail. Commented Mar 6 at 8:33