# Benford's Law and Data Spread

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Benford's law is the observation that for many datasets, the distribution of their first significant digit follows a nonuniform law given by:

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Contributed by: Stan Wagon (Macalester College) (March 2009)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The connection between Benford's law and the spread of the data is lucidly described in [1] (see also Chapter 21 of [3] and Chapter 1 of [3]). The idea is that when viewing a distribution in a base-10 log scale, the proportion of the axis corresponding to numbers beginning with 1 is . Hence, so long as there are several orders of magnitude, the error between this proportion and the proportion of the area lying above these numbers should be small.

[1] R. M. Fewster, "A Simple Explanation of Benford's Law," *The American Statistician,* 63(1), 2009 pp. 26-32.

[2] *Benford's Law: Theory and Applications*, edited by Steven J. Miller, Princeton: Princeton Univ. Pr., 2015.

[3] S. Wagon, *Mathematica in Action*, 3rd ed., New York: Springer, 2010.

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