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The subtleties of averages

Walter Krämer is Professor for Statistics in Dortmund and knows which facts best describe Germans, and which don’t.

Martin Orth, 22.06.2020
Photos of fans replace real spectators in the stadium
Photos of fans replace real spectators in the stadium © picture alliance/dpa

Professor Krämer, our topic is “Germany in general”. As a statistician, which figures and facts would you use to best describe the people in Germany?

Based on the usual parameters such as income, wealth, life expectancy, years of school education, or the number of children per family, people in Germany are refreshingly average in Europe. But in per capita beer consumption they have been overtaken by the Czech Republic and Austria. Exceptions are their love of cars, their love of their homeland and their enthusiasm for football. Germans move home far less often than people in other countries, such as in the USA. And with more than 7 million members and more than 26,000 clubs, the German Football Federation (DFB) is the world’s largest individual sport association. And the average number of spectators per match in the Bundesliga is higher than any other top league in Europe.

Statistics professor Walter Krämer, Technical University Dortmund
Statistics professor Walter Krämer, Technical University Dortmund
The Sauerkraut cliché is completely misleading.
Statistics professor Walter Krämer, Technical University Dortmund

You are known for treating your subject with a healthy sense of humour. Which often quoted figures used to describe people in Germany are quickly misleading?

Let’s start with the average size of a family at 1.3 persons. This clearly illustrates that the normal use of arithmetic averages results in values that simply don’t occur in real life. For instance, on average each German person has less than two legs, exactly 1.99999. And the Sauerkraut cliché is completely misleading. In Poland people eat more than twice as much Sauerkraut per capita compared with Germans. And a single American company in New York State produces more Sauerkraut each year than all of the producers in Germany combined.

When does the calculation of averages reach its limits as a method for describing complex issues? Or when are other parameters, such as extremes, more meaningful?

In the case of averages it’s always important to keep the deviations in mind. When three friends drink an average of five beers in an evening, it makes a big difference whether they all drink the same amount, or one of them drinks 15 beers and the others none. And sometimes averages are totally uninteresting. Who wants to know the average speed of the athletes running in the 100 metre sprint at the last Olympic Games? In this case people are far more interested in the extremes.

Interview: Martin Orth


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