If asked whether certain digits in numbers collected randomly from, for example, the front pages of newspapers or from stock-market prices should occur more often than others, most people would think not.
Figure 1. First significant digits in groups of numbers are popularly regarded to be distributed roughly equally between the nine nonzero integers. As the astronomer and mathematician Simon Newcomb noted in 1881, however, it is not always so. He found that the pages in a library book of logarithms were quite dirty with use in the 1s and progressively less so with higher digits. Newcomb was also able to develop an empirical formula predicting the probability of a particular digit’s appearance. More than 50 years later, Frank Benford rediscovered this phenomenon and found that it fit many different data sets. Since then, other investigators have found that data sets as diverse as stock-market or commodities prices—such as these displayed on a board reflecting activity on the floor of the Chicago Board of Trade—and census figures follow Benford’s law. Yet the phenomenon refused to submit to a rigorous mathematical proof until the mid-1990s—a development that has led to the law's proposed use by the Internal Revenue Service and in detecting accounting fraud.
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