R is for . . .

I'm posting Mad-Cool-Math Nuggets for the A to Z Challenge.

Image courtesy: Wikicommons

R is for random data. I got the idea for this blog from 5 Seriously Mind-Boggling Math Facts on the LiveScience website.

Consider all the street addresses in the United States, or the lengths of all the rivers in the world, or stock prices. What will the first digit of these numbers be? A random collection of the nine nonzero digits? Surprisingly not!

For many large collections of numbers, you will see that more of them start with the digit 1 than any other digit--about 30%. The next largest group will start with the digit 2, and so it goes down to 5% of the numbers starting with the digit 9. See the graph above.

You can read more about Benford's Law here. Large sets of numbers that do not follow Benford's law do exist, such as telephone numbers.

Want to try a little test of Benford's law? If you aren't worried about security, put the number of your street address in the comments below. Any street address number will do: home, work, school, favorite bar. I'll start: 249.