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

Abstract

How accurately can final-year students majoring in statistics, physics, and finance label the vertical axis of a normal distribution, explain their label, identify units, and answer a question about the impact of horizontal-axis rescaling? Our survey finds that only 27 out of 148 students surveyed (i.e., 18.2%) could label the vertical axis of the normal distribution correctly, and of these, only five students (i.e., 3.4%) could explain their label. Performance on individual survey questions differed by degree program, as might be expected, but overall survey performance varied very little, ranging between only 8.8% and 12.5% of survey questions answered correctly across degree programs. Common misconceptions included labeling the vertical axis as "probability," "count," or "frequency." To address these demonstrated gaps in statistics education, we give counterexamples to show why these labels cannot be correct; we explain why "probability density" is the correct label; and we give an intuitive explanation of probability density and its units. We also discuss the impact of horizontal-axis rescaling, and we 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. This paper is intended for all levels of statistical education.

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

JEL Classification: A20