Project 3. First digits. Here is a remarkable fact: the first digits of the numbers in long tables are usually not equally likely to have any of the 10 possible values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The digit 1 tends to occur with probability roughly 0.3, the digit 2 with probability about 0.17, and so on. You can find more information about this fact, called “Benford’s law,’’ on the Web or in two articles by Theodore P. Hill, “The Difficulty of Faking Data,’’ Chance, 12, No. 3 (1999), pp. 27–31; and “The First Digit Phenomenon,’’ American Scientist, 86 (1998), pp. 358–363. You don’t have to read these articles for this project.

Locate at least two long tables whose entries could plausibly begin with any digit. You may choose data tables, such as populations of many cities, the number of shares traded on the New York Stock Exchange on many days, or mathematical tables such as logarithms or square roots. We hope it’s clear that you can’t use the table of random digits. Let’s require that your examples each contain at least 300 numbers. Tally the first digits of all entries in each table. Report the distributions (in percentages) and compare them with each other, with Benford’s law, and with the “equally likely’’ distribution.