10 February 2005

Not all numbers are equal

So dig this.
You might expect that there would be roughly the same number of numbers beginning with each different digit: that the proportion of numbers beginning with any given digit would be roughly 1/9. However, in very many cases, you'd be wrong!

Surprisingly, for many kinds of data, the distribution of first digits is highly skewed, with 1 being the most common digit and 9 the least common. In fact, a precise mathematical relationship seems to hold: the expected proportion of numbers beginning with the leading digit n is log10((n+1)/n).

This relationship, shown in the graph of Figure 1 and known as Benford's Law, is becoming more and more useful as we understand it better. But how was it discovered, and why on earth should it be true?

Very counterintuitive. Very cool. And, it turns out, there are a lot of applications.

No comments: