An experiment on the distribution of data

1. Find a list of at least 20 numbers (for example, a table of properties of the elements in a chemistry handbook).
   • These should be empirical data, not artificially constructed numbers such as phone numbers.
   • They should span several orders of magnitude, not be tightly bunched like student GPRs.
2. On an axis or a ruler, plot the numbers with the first digit removed. (Ignore the location of the decimal point.) The distribution should be roughly uniform, since the second digit is completely random.
3. Plot the numbers intact. (Ignore the location of the decimal point.) You should find them strongly bunched to the low end (e.g., many more numbers begin with 1 than with 9).
4. Plot the intact numbers on a logarithmic scale. (Ignore the location of the decimal point.) The distribution should now be uniform!
   • To do this step without logarithmic graph paper: Take the logarithm of each number to the base 10, discard the part before the decimal point, and plot what's left on a regular scale.
   • Or construct your own logarithmic scale, or copy it from your grandfather's slide rule.
5. This result makes sense if you think about what happens when you put the decimal point back in. The number of data points between 10 and 11 ought to be roughly the same as the number between 9 and 10, right? But if the data really span several orders of magnitude randomly, then the number between 10 and 11 should be about the same as the number between 1.0 and 1.1, and that is far fewer than the total number between 1 and 2.