where: n = the first significant digit of a number
Notice that if a data entry (base 10) begins with a 1, the entry has
to be at most doubled to have a first significant digit of 2. However, if a data entry
begins with a 9, it only has to be increased by, at most, 11% to change the
first significant digit into a 1. This once again illustrates that a first
significant digit of 1 is
more likely to occur than a 9.
Benford's law has been used as a method for spotting
fraudulent accounting data by looking at the first significant digit of each data entry
and comparing the actual frequency of occurrence with the predicted
frequency. Most white collar criminals are unaware of Benford's law and will
use each digit about 10% of the time for the first significant digit in a number.
Benford's law doesn't work for numbers
controlled to a specific value, nor does it work for truly random numbers
such as those generated by a random number generator.
Benford's law also doesn't work well for small sample sizes. However, it
holds true in a surprising number of situations. Benford's
law shows that natural processes can be remarkably resistant to
complete randomness.
References:
1. "Following Benford's Law, or Looking Out for No. 1",
By Malcolm W. Browne (From The New York Times, Tuesday, August 4, 1998)
2. "The FirstDigit Phenomenon" by T. P. Hill, American Scientist, JulyAugust 1998)
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