Benford's law

Frank Benford published a rule in 1938 (that had been identified by Simon Newcomb, in 1881) that 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 several scientific constants 

the 'numberphile' youtube clip