Benford's Law

Overview

Objectives/Goals To test the validity of Benford's Law and how it can be applied in real life situations. Methods/Materials Materials List 1. Microsoft Excel 2. Various statistics from The World Almanac 3. Vital Statistics of the United States Volume II-Mortality 4. Random Number Table 5. Various articles on the internet Procedures 1. Collect various data from World Almanac 2. Put this data into an Excel spreadsheet. 3. Using various formulas, isolate the left most digit. 4. Then count the number of times, each digit appears. 5. Graph the data. 6. See if the data follows the Benford#s Law distribution. 7. Test whether or not truly random numbers from a random number table and data, which is bounded fit the distribution. Repeat procedures 2-6. 8. Test whether or not things such as land area still fit the distribution even after being converted to another unit. Repeat procedures 2-6. Results Benford's Law does in fact apply. However, certain sets of data does not conform to Benford's Law namly, data which is bounded by a maximum and minimum, numbers randomly generated by a person, assigned numbers, and numbers taken from a random number table. Conclusions/Discussion The data collected from this experiment supports the hypothesis given to a certain extent. Various data such as World Wheat Production and US Air Quality of certain cities all shows a conformation to Benford's Law. However, data such as SAT scores and human generated numbers showed that it does not conform to data which is bounded or generated in such a manner.

Competition history

• CSEF 2004 Mathematics & Software · Entry S1215

Resources

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