  We report the existence of deterministic patterns in plots showing the
relationship between the mean and the Fano factor (ratio of variance and mean)
of stochastic count data. These patterns are found in a wide variety of
datasets, including those from genomics, paper citations, commerce, ecology,
disease outbreaks, and employment statistics. We develop a theory showing that
the patterns naturally emerge when data sampled from discrete probability
distributions is organised in matrix form. The theory precisely predicts the
patterns and shows that they are a function of only one variable - the sample
size.
