Maths prize, 21 October 2016

benford

Students were asked to investigate Benford’s Law. Maz Razwan won the prize, by showing that the quantities of anything that grows exponentially (like a culture in a petri dish) will find their first digits following Benford’s Law.

That’s true regardless of what units the quantities are measured in.

See also Zipf’s law.

Any quantity X where log X is distributed uniformly (i.e. the probability of log X being between a and a+b is [for a given b] the same for every a) will find its first digits following Benford’s Law, as shown below. But that’s the same as saying: any quantity X where the probability of a certain % increase is the same whatever the level that X has reached.

Introduction to Benford’s Law

Worksheet on the maths of Benford’s Law

More maths and more background on Benford’s Law