Benford's Law
Main Concept

Benford's law was discovered in 1881 when Simon Newcomb, an American astronomer, noticed that the early pages of books of logarithms were more worn than the later pages. He concluded that numbers with small first digits naturally occur more frequently than numbers with larger first digits. In 1938, Frank Benford, a physicist, observed this property in other data sets. Benford's law has been used to uncover fraud, because people producing fake data generally choose numbers whose first digits are more uniformly distributed than would naturally occur.



Choose a data set and see how Benford's law applies to it. For each data set, the number of elements with a given leading digit is shown, and its percentage of the entire data set is computed. You can compare the actual values with the numbers predicted by Benford's law, which states that the expected percentage of the $d$ as the leading digit in a collection of measurements is ${\mathrm{log}}_{\mathit{10}}\left(\mathit{1}\mathit{\+}\frac{\mathit{1}}{d}\right)$.
Leading Digit

Count

% of Total

Benford's Law %${}$




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