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Math · Intermediate

Power Laws & Surprising Statistics

Some of the strangest patterns in data come from power laws and scale invariance. Discover Benford's law of first digits, Zipf's law of word frequencies, how log–log plots reveal hidden power laws, why heavy-tailed data makes the average a treacherous guide, and how "the rich get richer" creates power laws.

7 lessons~35 min0/7 complete
Start courseHelpful background: Statistics
1

Strange Patterns

First digits and word ranks.

  1. Benford’s LawThe surprising first digit
  2. Zipf’s LawRank times frequency
2

Power Laws

Straight lines on log scales, and heavy tails.

  1. Log–Log PlotsRevealing hidden exponents
  2. Heavy TailsWhen the average misleads
3

Where Power Laws Come From

Broken averages and runaway growth.

  1. When Averages FailThe law of large numbers breaks
  2. The Rich Get RicherPreferential attachment
  3. Aftershocks & Omori’s LawA power law in time