# What Quantity Appears on the Vertical Axis of a Normal Distribution? A Student Survey

19 Pages Posted: 27 Aug 2018 Last revised: 4 Feb 2020

See all articles by J. Scott Chaput

## J. Scott Chaput

University of Otago - Department of Accountancy and Finance

## Timothy Falcon Crack

University of Otago - Department of Accountancy and Finance

## Olena Onishchenko

University of Otago

Date Written: February 4, 2020

### Abstract

Final-year students in statistics, physics, and finance were asked to label the vertical axis on a normal distribution, explain their label, identify units, and answer a question about the impact of x-axis rescaling. Fewer than 4% of the students could both label the vertical axis correctly (as probability density) and explain their label. The most common incorrect vertical axis label was “probability.” Performance on individual survey questions differed significantly by academic discipline, but overall survey performance varied very little, ranging between only 8.8% and 12.5% of survey answers being correct across disciplines. To fill these demonstrated gaps in statistics education, we give counterexamples to demonstrate why “probability” cannot be the correct vertical axis label; we explain why “probability density” is the correct label; and we give an intuitive explanation of probability density and its units. We also indicate how the units of probability density change if the probability density function is for a bivariate or trivariate distribution instead of a univariate distribution, and we discuss the impact of x-axis rescaling. This paper is intended for all levels of statistical education.

Keywords: probability density; linear denisty; pdf; pmf; cdf; resclaing

JEL Classification: A20

Suggested Citation

Chaput, J. Scott and Crack, Timothy Falcon and Onishchenko, Olena, What Quantity Appears on the Vertical Axis of a Normal Distribution? A Student Survey (February 4, 2020). Available at SSRN: https://ssrn.com/abstract=3229568 or http://dx.doi.org/10.2139/ssrn.3229568

## Paper statistics 