Evaluating Benford’s Law
Grade Level: 9th to 12th; Type: Mathematics/Computer Science
This experiment will investigate the applicability of Benford’s Law to many sets of everyday data.
- For which types of data is Benford’s Law valid?
- Are there certain types of data sets that do not conform to Benford’s Law?
Benford's Law, also called the first-digit law, describes how in lists of numbers from many everyday sources of data, the leading digit is distributed in a specific, predictable way. This experiment will evaluate many sources of data to see if Benford’s Law holds true.
- Many real-life sources of data
- Graphing software
- Notebook for analyzing results
- Gather many large datasets. Examples of data could include: A list of every country and its population; income tax returns;utility bills; distance of stars from the Earth in light years.
- Tally the leading digit of every number you encounter in a dataset. This can be done on a computer using Microsoft Excel (see the second reference, below).
- Create a bar graph demonstrating the frequency of each leading digit (1 to 9) in the dataset.
- Analyze your results. Do the numbers in your data set conform to Benford’s Law? The expected percentage of numbers starting with each digit is: 1: 30.1%; 2: 17.6%; 3: 12.5%; 4: 9.7%; 5: 7.9%; 6: 6.7%; 7: 5.8%; 8: 5.1%; 9: 4.6%
- Repeat your analysis for other sets of data. Do all of your datasets appear to conform to Benford’s Law? What types of datasets do not follow Benford’s Law?
Terms/Concepts: Benford’s Law
- Benford, F. 1938. The law of anomalous numbers. Proceedings of the American Philosophical Society 78:551.
- Lynch, A. and Xiaoyuan, Z. “Putting Benford’s Law to Work.”
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