Abstract
Joining previous authors, we propose axiomatic properties that yield the mean as the unique measure of center of a data set. In addition to familiar properties such as symmetry, homogeneity, and translativity, we make use of a condensation principle, first considered by Bemporad, that ties together means for different sample sizes and identifies an important physical characteristic of the center of mass of a body.
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Gray, J.E., Vogt, A. Axiomatics for the mean using Bemporad’s condition. Aequat. Math. 89, 1415–1431 (2015). https://doi.org/10.1007/s00010-014-0305-3
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DOI: https://doi.org/10.1007/s00010-014-0305-3