I was watching this serial called “NUMB3RS” the other night and I heard about this interesting stuff called the Benford’s law. Apparently, someone by name Newcomb (1881) observed that the first pages of logarithmic tables were more worn than the rest of the pages. Dr Benford (1938) later formulated it as a theory based on his findings that the number “1” appeared with a probability of 30% in most of the statistics, logarithmic tables and so on. This is much higher than the anticipated 11% if things were uniformly distributed among the numbers 1 to 9. In 1996, Dr.Hill proved Benford’s law with a formula for the probability (log (1+1/D) base 10), where D is the digit.
All this means is that, if you pick any kind of random list of tables or data, the number 1 appears more often than it is probabilistically predicted (somehow 0 is omitted). This is called the first digit phenomenon or the first digit law or leading digit phenomenon. The interesting outcome of this law is useful in analysing financial reports, income tax returns, statistical tables and most of the naturally generated data. If you try to plug-in your “made-up” numbers into any of these, it may not make up the same distribution as predicted by Benford’s law. So, if you are cooking up numbers, you better know what you are doing..:)..
Leading digit Probability (from Benford’s law)
1 30.1%, 2 17.6%, 3 12.5%, 4 9.7%, 5 7.9%, 6 6.7%, 7 5.8%, 8 5.1%, 9 4.6%