Benford's Law.. WTH?

[Lanius]

http://en.wikipedia.org/wiki/Benford's_law

Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) 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 about 30% 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 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale.

Why the hell is it so?

[makattak]

Not sure of the mechanism, but because we are in base ten (10), the 1 represents the beginning of all increases in magnitude. (1,10,100,1000,10000, etc...)

Thus, in any list that measures items is likely to have 1 more than anything else because if you spill over into the next magnitude, you increase the chances of 1 being the first digit by a significant amount. (From 1-99, the chances of 1 being the first digit is .11. From 1-199, the chances of 1 being the first digit is .555, from 1-1999, the chances of 1 being the first digit is .5555... etc...)

So, a 30% chance can make sense. (Increase 1-299, the chance of a 1 is .37, 1-399, the chance is .2775, all the way until we get back down to .111)

The pattern for the rest of the digits in that article bear this out, as well.

[Lanius]

Huh.. that almost makes sense. Still, it's weird..

[vaskidmark]

http://en.wikipedia.org/wiki/Benford's_law

Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) 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 about 30% 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 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale.

Why the hell is it so?

Because most of the time folks look at you/read your exposition like you had some strange vegetable growing out of the top of your head if your list begins with

And second of all ....

or

"the three most common <fill in the blank> are:
2 -
3 -
4 -

stay safe.

[AZRedhawk44]

I imagine that "1" happens a lot less than 30% of the time in hexadecimal based systems (but still more than 1/16th of the time), and more than 50% of the time in binary systems.