Scholars often consider the arithmetic mean as the only mean available. This gives rise to several mistakes. Thus, in a first course in statistics, it is necessary to introduce them to a more general concept of mean. In this work we present the notion of mean suggested by Oscar Chisini in 1929 which has a double advantage. It focuses students' minds on the substance of the problem for which a mean is required, thus discouraging any automatic procedure, and it does not require a preliminary list of the different mean formulas. Advantages and limits of the Chisini mean are discussed by means of examples.
How to compute a mean? The Chisini approach and its applications
GRAZIANI, REBECCA;VERONESE, PIERO
2009
Abstract
Scholars often consider the arithmetic mean as the only mean available. This gives rise to several mistakes. Thus, in a first course in statistics, it is necessary to introduce them to a more general concept of mean. In this work we present the notion of mean suggested by Oscar Chisini in 1929 which has a double advantage. It focuses students' minds on the substance of the problem for which a mean is required, thus discouraging any automatic procedure, and it does not require a preliminary list of the different mean formulas. Advantages and limits of the Chisini mean are discussed by means of examples.
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