Geometric standard deviation is the degree of variance of a particular group of numbers from the geometric mean as opposed to the binomial mean. It is appropriately used for numbers that form a geometric distribution rather than a binomial one.
Geometric standard deviations are used in applications such as determining the variance of a success of trials. For example, in calculating deviations for such things as the compound annual growth rate, a geometric standard deviation is the proper method. It is calculated by taking the logarithm of each value and the logarithm of the comparison value, comparing the logs, and then using those numbers in the standard deviation formula to arrive at the geometric standard deviation.