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