The Weight of Euro Coins: Its Distribution Might Not Be As Normal As You Would Expect

Abstract

Classical regression models, ANOVA models and linear mixed models are just three examples (out of many) in which the normal distribution of the response is an essential assumption of the model. In this paper we use a dataset of 2000 euro coins containing information (up to the milligram) about the weight of each coin, to illustrate that the normality assumption might be incorrect. As the physical coin production process is subject to a multitude of (very small) variability sources, it seems reasonable to expect that the empirical distribution of the weight of euro coins does agree with the normal distribution. Goodness of fit tests however show that this is not the case. Moreover, some outliers complicate the analysis. As alternative approaches, mixtures of normal distributions and skew normal distributions are fitted to the data and reveal that the distribution of the weight of euro coins is not as normal as expected.