It's called
median absolute deviation (MAD)
http://en.wikipedia.org/wiki/Median_absolute_deviation

Standard deviation
http://en.wikipedia.org/wiki/Standard_deviation
and its square, Variance
http://en.wikipedia.org/wiki/Variance
are much nicer and more natural in terms of their properties, see e.g.
http://en.wikipedia.org/wiki/Variance#Basic_properties
http://en.wikipedia.org/wiki/Standard_deviation#Identities_and_mathematical_properties

For more fun, see here
http://en.wikipedia.org/wiki/Metric_(mathematics)
http://en.wikipedia.org/wiki/Norm_(mathematics)