NAME: The Weight of Euro Coins TYPE: Fitting distributions to data SIZE: 2000 observations, 3 variables DESCRIPTIVE ABSTRACT: In many statistical models the normal distribution of the response is an essential assumption. This paper uses a dataset of 2000 euro coins with information (up to the milligram) about the weight of each coin. 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. Mixtures of normal distributions and skew normal distributions are fitted to the data, revealing that the normality assumption might not hold for those weights. SOURCE: The data were collected by Herman Callaert at Hasselt University in Belgium. The euro coins were "borrowed" at a local bank. Two assistants, Sofie Bogaerts and Saskia Litiere weighted the coins one by one, in laboratory conditions on a weighing scale of the type Sartorius BP 310s. VARIABLE DESCRIPTIONS: Columns 1 - 8 ID this is the case number 9 - 16 weight weight of the euro coin in grams 17 batch number of the package Values are aligned and tab-delimited. There are no missing values STORY BEHIND THE DATA: Curriculum reform in Flanders (the Flemish part of Belgium) resulted in a significant increase of statistical topics in grades 8-12. A group of university professors and high school teachers took this opportunity for reshaping statistics education towards "more concepts and more real data". In Belgium, as in many countries in Europe, the introduction of the Euro has had a major impact on the life of people. That's why it was decided to study a characteristic (the weight) of the "Belgian 1 Euro" coin, and use this dataset in schools. PEDAGOGICAL NOTES: This dataset may be explored by students at several levels. In high school, graphical methods can be used, perhaps in conjunction with a simple goodness of fit test. Also the story behind the data gathering process, and the lesson to be learned here, is crucial in any real life statistical experiment. A first year college course could delve a bit deeper, while a full analysis (introducing mixtures and the skew normal) can be revealing in a second course in statistics. SUBMITTED BY: Ziv Shkedy, Marc Aerts, Herman Callaert Hasselt University Center for Statistics Agoralaan, 3590 Diepenbeek, Belgium marc.aerts@uhasselt.be