Posted by
Aku
at
5:02 PM
Benford's law states that the leading digit d (d ∈ {1, …, b − 1} ) in base b (b ≥ 2) occurs with probability proportional to logb(d + 1) − logbd = logb((d + 1)/d). This quantity is exactly the space between d and d + 1 in a log scale.
In base 10, the leading digits have the following distribution by Benford's law, where d is the leading digit and p the probability:
| d | p |
| 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% |