Investigating statistical laws that govern seemingly random or chaotic datasets.
Benford's Law (The First-Digit Anomaly)
Benford's Law says that in many real-world datasets, numbers are much more likely to begin
with smaller digits than larger ones. About 30% begin with 1, while fewer than 5% begin with
9 — not the roughly even 11.1% each digit would get if first digits were random. Choose
a dataset below and watch how its first digits compare with Benford's prediction.
Purple bars show the selected sample. Amber marks show Benford's predicted
first-digit percentages.
Observed
Benford reference
30.1%
numbers beginning with 1
Benford predicts 30.1%
4.6%
numbers beginning with 9
Benford predicts 4.6%
6.5×
how much more often 1 appears than 9
Benford predicts 6.6×
2 · Additional details
What is happening behind the bars?
—
approximate numeric range
—
orders of magnitude spanned
Benford's first-digit regions on a logarithmic scale
The lesson:
Benford's Law is not a rule that every dataset must obey. It works best for certain kinds
of naturally occurring, wide-ranging or multiplicative data. Assigned numbers and tightly
constrained values can behave very differently.