The prisoner sex-ratio dispersion index is the natural logarithm (log) of the ratio of the third to the first quartile in the distribution of prisoner sex ratios. That’s equivalent to the log of the third quartile minus the log of the first quartile. Since log is a monotonic function, the quartiles in the prisoner sex-ratio distribution correspond to the quartiles in the distribution of log sex ratios. The later are approximately normally distributed. Moreover, in a normal distribution, the difference between the third and first quartiles (the interquartile range) is proportional to the standard deviation. The sex-ratio dispersion index is thus proportional to the standard deviation in the log sex-ratio distribution.
The sex-ratio dispersion index is a simple, scalar measure of the dispersion of a sex-ratio distribution. The sex-ratio dispersion index and the median sex ratio (which is a median-unbiased estimator of the mean of the log sex-ratio distribution) are approximately sufficient statistics for describing the sex-ratio distribution.