What is the Law Of Large Numbers?

John Spacey, updated on February 02, 2018

The law of large numbers states that results will be as expected after a large number of samples. In other words, an experiment with a small number of samples may have unpredictable results but after a large number of samples results become more predictable.

Consider a tourist who visits New York City and witnesses a terrible crime. The tourist may develop an exaggerated sense of how dangerous the city is compared to their hometown. If the tourist later moves to New York for their job, their experience in the city will become more normal with time. After a large number of days, they are likely to view the crime rate differently as opposed to a single day experience.

A small number of samples results tends to yield random observations. Over a large number of samples, a pattern will become clear if one exists.

Often Misused

The term Law of Large Numbers is specific to sample sizes in experiments. It is often confused with other effects such as the challenges faced by large organizations. For example, if a large company has trouble growing this is typically related to Diseconomies of Scale as opposed to the Law of Large Numbers.

Overview: Law Of Large Numbers
Type	Statistical Analysis
Definition	If a pattern exists it will become clear after a large number of samples. A small number of samples is likely to be random.
Related To	Regression Toward The Mean Proof By Example
Often Confused With	Diseconomies Of Scale