An interactive explorer for Benford's Law across real datasets
4 hours ago
- #First-digit phenomenon
- #Statistical anomaly
- #Benford's Law
- Benford's Law states that in many real-world datasets, the leading digit is not uniformly distributed.
- The digit 1 appears as the first digit about 30% of the time, while digit 9 appears less than 5%.
- This phenomenon occurs across diverse data, such as populations, river lengths, prices, and mathematical sequences like Fibonacci.
- The law has a logarithmic formula: P(d) = log10(1 + 1/d), where d is the first digit.
- It was discovered by Simon Newcomb in 1881 and later studied by Frank Benford in 1938, who collected 20,229 data points.
- Theodore Hill proved it rigorously in 1995, showing it arises from mixtures of distributions.
- Scale invariance explains Benford's Law: the distribution remains unchanged under unit conversion.
- Applications include fraud detection, as fabricated data often deviates from Benford's distribution.
- Real-world examples include analyses of the 2009 Iranian election, Enron's financial data, and Greek national statistics.
- The law does not apply to data confined to a narrow range, such as adult heights or constructed identifiers.