Benford's Law
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Example: among the first thousand powers of 2 (2, 4, 8, 16, …), how many start with 1? Pick another sequence or paste your own data to compare with Benford.
Step by step
What each term means
- Chance of the First Digit (P(d))
- The probability that a number starts with digit d, from 1 to 9: about 30% for 1 and under 5% for 9.
- Base-10 Logarithm
- Measures where the number falls within its decade, on a logarithmic ruler. It is on that ruler that numbers spread over several orders of magnitude become uniform.
- From d to d + 1 ((1 + 1/d))
- The piece of the decade between d and d + 1, measured in logarithm: from 1 to 2 is log₁₀ 2 ≈ 30%; from 9 to 10, only log₁₀(10/9) ≈ 4.6%.