There is a kurtosis measure, a fourth moment as standard deviation is a second moment, for this variation.
kurtosis is a measure of the peakedness of the distribution.
British Dictionary definitions for kurtosis
(statistics) a measure of the concentration of a distribution around its mean, esp the statistic B2 = m4/m2² where m2 and m4 are respectively the second and fourth moment of the distribution around the mean. In a normal distribution B2 = 3 See also platykurtic, mesokurtic, leptokurticCompare skewness