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Slepkov, AD, Ironside, KB and DiBattista, D (2015)

Benford’s Law: Textbook Exercises and Multiple-Choice Testbanks

PLoS ONE 10(2): e0117972.

ISSN/ISBN: Not available at this time. DOI: 10.1371/journal.pone.0117972

Abstract: Benford’s Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common leading digit is 1, with an expected frequency of 30.1%, and the least common is 9, with an expected frequency of 4.6%. Currently, the most common application of Benford’s Law is in detecting number invention and tampering such as found in accounting-, tax-, and voter-fraud. We demonstrate that answers to end-of-chapter exercises in physics and chemistry textbooks conform to Benford’s Law. Subsequently, we investigate whether this fact can be used to gain advantage over random guessing in multiple-choice tests, and find that while testbank answers in introductory physics closely conform to Benford’s Law, the testbank is nonetheless secure against such a Benford’s attack for banal reasons.

@article {, AUTHOR = {Slepkov, Aaron D. and Ironside, Kevin B. and DiBattista, David}, TITLE = {Benford’s Law: Textbook Exercises and Multiple-Choice Testbanks}, JOURNAL = {PLoS ONE}, YEAR = {2015}, VOLUME = {10}, NUMBER = {2}, DOI = {10.1371/journal.pone.0117972}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): General Interest, Mathematics Education