don steward
mathematics teaching 10 ~ 16

Tuesday, 28 December 2010

Benford's law

Frank Benford published a rule in 1938 (that had been identified by Simon Newcomb, in 1881) that e.g. if you look at a large enough sample of real data e.g. people's house numbers, around a third of the numbers will start with a 1

remarkably, the frequency of the numbers of digits, d, usually follows a log law:

F(d) = log(1 + 1/d)

values from this (theoretical) frequency distribution are shown above

students could see how this distribution compares with
real-life data e.g.
  • house numbers of people in their class or year group
  • populations of cities in a country
  • lengths of longest rivers in the world
  • populations of countries in the world
  • lead digits of scientific constants 
the 'numberphile' youtube clip

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