Benford's Law - Empirical approach

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The historical backgroundsection mentions several examples of data sets distributed according to Benford`s distribution. Especially when the topic is covered in class, it should not stop with just presenting such examples to students. Students should get the chance to examine the distribution of the first digit in data sets available to them. By this they actively engage in class because they will observe by counting themselves, that the initial digits are not uniformly distributed. This seemingly paradoxical result will leave a lasting impression and increase their interest. Such analysis of data sets are a great opportunity for a computer evaluation. A computer allows the evaluation of large data sets in relative short time, which would be barely possible by hand.

If such an experiment was done in class it would also be possible to analyze relatively large data sets by dividing it among the students. One possibility would be to bring one or more newspapers to class, where students are to pick any page and assess the frequencies of the single first digits of all numbers on that page.[1]The empiric frequencies discovered can be compared to the Benford probabilities.

Problem: An empiric study (**)

• Assess the initial digit distribution of the file sizes on your hard drive or just several folders by the „Benford.exe“program!
• Create in EXCEL the first 100 Fibonacci numbersand assess the frequencies of the first digits. Present those frequencies graphically in EXCEL!
  OR: Carry out an empiric survey of a data set of your choice and present the frequencies graphically! Use the spreadsheet software EXCEL for your evaluation!

Problem: Choosing suitable data sets (**)

Let`s say you want to do an empiric examination of Benford`s Law with your class. What should you pay attention to, as you chose data sets to be examined?

Give three examples each for data sets where you expect a Benford distribution or where you don`t expect a Benford distribution!

Problem: Catalogue (***)

What distribution do you expect if you would examine all initial digits of prices in any catalogue of a supermarket, a furniture store or a computer sales place? Are all the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 equally common?

Check what you guessed on any catalogue!