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Answers

•  Introduction  •  Introduction (cont.)   
•  Benford's Law and the IRS  •  The Math  •  The Answers

  1. The height of all 5th grade students in the U.S. measured in inches.

    No. In the U.S., the average height for both 10 year-old boys and girls is about 55 inches. This suggests that this data set would have a large clump in the middle of the distribution and trail off on either side.  We would certainly expect that there are no children, in this age range, whose height is between 0 and 42 inches, and likewise, we wouldn’t expect a 10 or 11 year-old to be taller than 70 inches. Therefore, the distribution would be between 4 and 6.
     

  2. The zip codes of all American CEOs.

    No. Zip codes do not have dimension and are more or less evenly distributed through the U.S., so we would not expect to see this data set converge to Benford’s law.

  3. The number of "hits" a random 6-digit number has in a Google search.

    Yes. Recent trials suggest that this set does fit with Benford’s law.  The searches have dimension (sites) and sufficient magnitude (can go from, presumably, 1 to as high as there are sites on web).

  4. Random numbers guessed by 100 incoming college freshmen.

    No. Random guess numbers have been shown to not fit Benford’s law.  People’s biases toward numbers prevent there from being any ‘rule’ that shows a distribution other than a relatively flat distribution where all number are used approximately the same number of times.  More-over, random numbers do not have dimension, so should automatically be excluded from Benford’s law.

  5. The population, at 1 hour intervals, in a bacterial culture.

    Yes. Since the population will grow exponentially, this data set would be expected to fit with Benford’s law. The data has dimension and the population can grow from 2 to whatever the carrying capacity of the Petri dish is.

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