### Slepkov, AD, Ironside, KB and DeBattista, D (2013)

#### Benford's Law: Textbook Exercises and Multiple-choice Testbanks

Preprint posted on physics arXiv - submitted 19 November 2013.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

**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%. The history and development of Benford's Law is inexorably linked to physics, yet there has been a dearth of physics-related Benford datasets reported in the literature. 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:**

```
@unpublished{,
AUTHOR = {Aaron D. Slepkov and Kevin B. Ironside and David DiBattista},
TITLE = {Benford's Law: Textbook Exercises and Multiple-choice Testbanks},
MONTH = {November},
YEAR = {2013},
DATE = {November 19, 2013},
EPRINT = {arXiv:1311.4787v1 [physics.data-an]},
URL = {http://arxiv.org/abs/1311.4787},
NOTE = {Last accessed December 3, 2014},
}
```

**Reference Type:** Preprint

**Subject Area(s):** General Interest