In physics multiple choice papers, the correct answers should follow Benford's law while the other options should not. So can an enterprising student use this to beat the test?
Back in the 1930s, the American physicist Frank Benford discovered that the first digit in certain lists of numbers was much more likely to be a 1 than a 9. He tested this idea on a variety of datasets such as the surface area of rivers, a list of physical constants and even the street addresses of the first 342 entries in American Men of Science.
In each case, he found the same pattern. That the number 1 is the first digit 30 per cent of the time, the number 2 is the first digit 18 per cent of the time, the number 3 is first 13 per cent of the time and so on until the number 9 which is first only 5 per cent of the time.
He went on to propose Benford's Law: that the distribution of first numbers in many, but not all, datasets follows the same logarithmic pattern. It turns out that this property is true of many dataset involving physical quantities but is not true of randomly generated numbers in which the distribution of first digits is uniform.
Now, 60 years later, Benford's law is famous. It's best known application is in uncovering fraud. That's possible because the distribution of first digits in a company's accounts turns out to follow Benford's law. So any deviation from this is good evidence that somebody has been cooking the books. And this has led to the downfall of various fraudsters. |