Variance/mean ratio (VMR) is used to characterize the distribution of events or objects in time or space. If the distribution is random - i.e. can be modeled by the Poisson process or its multidimensional analogues - then, the VMR is about 1.0. Larger values (VMR >1.0) correspond to existence of "clumps" - spatial or temporal clusters. Smaller values (VMR < 1.0) correspond to a more-uniform-than-random distribution (often named "even", "uniform") - i.e. mutual "avoidance" of events or objects in time or space.
These properties of VMR stem from the fundamental property of the Poisson distribution that the variance and the mean are equal.
The VMR is used in Variance/Mean Ratio test .