### 8.4 Expecting the Unexpected

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• Math Help

Benford's law is named after physicist Frank Benford (1883-1948), who stated it in 1938. It should be noted that the law had been previously stated by astronomer and mathematician Simon Newcomb (1835-1909) in 1881. Benford's law is also called the first digit law.

In Benford's law, note that the probability that a leading digit is 1 is 30.1%. This is almost 3 times greater than the expected probability of In fact, you would expect the probability of each of the 9 digits to be about 11.1%. According to Benford's law, however, this is not the case, as shown in the table.

• Consumer Suggestion

The show NUMB3RS employed mathematical consultants to write the math equations that appear in the show, and verify the accuracy of each episode. Check out this website sponsored by Cornell University that features materials based on the mathematics behind each episode of NUMB3RS.

• Checkpoint Solution

A computer program can be used to analyze the first digits of the various numbers on a tax form. The frequency of each first digit in the tax return can be compared to the expected frequency according to Benford's law. If there are any unusual results, the filer can be investigated further.

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``` ______    _    _     ______    _____    _    _
|      \\ | || | ||  /_____//  |  ___|| | \  / ||
|  --  // | || | ||  `____ `   | ||__   |  \/  ||
|  --  \\ | \\_/ ||  /___//    | ||__   | .  . ||
|______//  \____//   `__ `     |_____|| |_|\/|_||
`------`    `---`    /_//      `-----`  `-`  `-`
`-`
```