Benford's Law states that if d is the first digit of a number occuring in real life, that digit should occur with probability P(d) = lg (d+1) - lg d. The space between log scales.
P(1) = lg 2 - lg 1 = 0.301
P(2) = lg 3 - lg 2 = 0.176
P(3) = lg 4 - lg 3 = 0.125
P(4) = lg 5 - lg 4 = 0.097
P(5) = lg 6 - lg 5 = 0.079
P(6) = lg 7 - lg 6 = 0.067
P(7) = lg 8 - lg 7 = 0.058
P(8) = lg 9 - lg 8 = 0.051
P(9) = lg 10 - lg 9 = 0.046
What does this imply??? If you were to compile all the numbers in your bank books and if were to take a look at the first digit, they should follow this distribution in the long run. This is a way that IRS have learnt to spot people who fudge numbers in their books. People who fake their numbers tend to distribute their numbers more "randomly" but thats not true in real life.
Its actually quite counter-intuitive as people assume that if numbers are random, they should be equally distributed. However, numbers in real life are not completely random. Numbers starting with '1' occurs more than 6 times more than '9'.
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