Solution
Benford's Law
Show the problem again
In many naturally occurring datasets (populations, financial figures, physical constants), what fraction of numbers have leading digit 1, according to Benford's Law? Answer as a percentage rounded to one decimal place, or give the exact expression.
Worked solution
The answer is log₁₀(2) ≈ 30.1%. Benford's Law states P(leading digit = d) = log₁₀(1 + 1/d), giving 30.1% for d = 1 down to 4.6% for d = 9. It arises when data spans several orders of magnitude and is scale-invariant: quantities spend more "logarithmic time" between 1 and 2 than between 8 and 9. Forensic accountants use deviations from Benford to flag fabricated figures.
Source: First observed by Simon Newcomb (1881) and rediscovered by Frank Benford (1938). Statement written for AxiomIQ.