The Fano Factor is a statistical measure used to describe the variability of a discrete random variable. It is defined as the ratio of the variance of the count of events to the mean of those events. This factor helps in understanding the degree of fluctuations in a system, particularly in fields like physics and biology. In many applications, a Fano Factor greater than one indicates over-dispersion, meaning the data is more variable than expected for a Poisson process. Conversely, a Fano Factor less than one suggests under-dispersion, where the data is less variable. This concept is crucial for analyzing count data in various scientific studies.