Open any random data set — populations, river lengths, stock prices, address numbers. Look at the first digit of each. You'd expect 1 through 9 to show up equally. They don't.
Quick check
Across many natural data sets, roughly what fraction of values have **1** as their first digit?
Benford's leading-digit odds
- Starts with 1 → ≈ 30%
- Starts with 2 → ≈ 18%
- Starts with 3 → ≈ 12%
- Starts with 9 → ≈ 4.6% — the rarest leader
Your turn
Why doesn't Benford's Law apply to, say, human heights in centimetres?
Tax-fraud and election auditors run Benford checks: invented numbers tend to have suspiciously uniform first digits — a red flag.
Benford's Law
About 30% of numbers start with 1. Only 5% start with 9. The smaller the digit, the more often it leads. It's a rule found in nature, not a theorem someone invented.
Tax fraud investigators use Benford's Law. Faked numbers usually have too-uniform first digits — a giveaway.