Benford's Law

[wellinghall]

Benford's law states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty. The basis for this law is that the values of real-world measurements are often distributed logarithmically, thus the logarithm of this set of measurements is generally distributed uniformly.

This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws. The result holds regardless of the base in which the numbers are expressed, although the exact proportions change.

http://en.wikipedia.org/wiki/Benford%27s_law

Comments

[philmophlegm.livejournal.com]

This is something that auditors' sampling techniques take into account.

[wellinghall.livejournal.com]

Indeed.

[tovaglia.livejournal.com]

Interesting!

[wellinghall.livejournal.com]

I find it so, certainly! (And I haven't forgotten that I owe you emails!)

[asklepia.livejournal.com]

I've met this law before, and yes, it is most definitely counter-intuitive. I wonder how the proprtions change with the base notation? The wikipedia article didn't really go into that.

[wellinghall.livejournal.com]

I think they go by log(base), rather than log(10).