### 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.

**Bibtex:**

```
@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 = {http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0117972&representation=PDF},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** General Interest, Mathematics Education