An empirical statistical law or (in popular terminology) a law of statistics represents a type of behaviour that has been found across a number of datasets and, indeed, across a range of types of data sets.
There are other statistical and probabilistic theorems that also have "law" as a part of their names that have not obviously derived from empirical observations.
What distinguishes an empirical statistical law from a formal statistical theorem is the way these patterns simply appear in natural distributions, without a prior theoretical reasoning about the data.
For example, a ranked list of US metropolitan populations also follow Zipf's law,[8] and even forgetting follows Zipf's law.
[9] This act of summarizing several natural data patterns with simple rules is a defining characteristic of these "empirical statistical laws".