I'm trying to wrap my mind around Benford's Law.
According to wikipedia Benford's law applies in many "naturally occurring collections of numbers." It "applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, physical and mathematical constants,[3] and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude."
I think I understand it and have plenty of examples of how it works. And it makes sense. However, I tried out this website to see more examples to show my class.
http://www.testingbenfordslaw.com/most-common-iphone-passcodes
One of the examples, is iPhone passcodes which are 4 digits and I believe can start with any digits 0,1,2,3....9. According to the website, they are suggesting Benford's Law applies here.
To me, this doesn't seem like Benford's law applies here. It seems to me that generally speaking a person that chooses a random 4 digit number has an equally likely chance at choosing numbers that start with 0,1,2,3,4...9. All passcodes are 4 digits so there doesn't seem to be a span of "multiple order of magnitude". In addition, this doesn't seem to be "naturally occurring" to me, in the same sense of listing all the populations of cities in the world. In one sense it is naturally occurring because you are not instructing people to do anything but choose a number, but I can't figure out why I think its not naturally occurring in the same sense? Am I wrong?
What are your thoughts?