Contributed paper list
(Friday 18th, 10:55-12:25) In session C16B
Invariance and descriptive statistics
Presenter Guido del Pino
The main focus of teaching statistics at school is statistical literacy, which uses as little mathematics as possible. This fact, together with an unappealing training emphasizing scattered definitions and computational recipes, makes mathematics teachers to strongly dislike statistics. Although the main issue is statistical literacy, providing an underlying mathematical structure for the statistical concept should help making the subject more interesting to mathematically trained people. It is shown that the mathematical concepts of invariance and equivariance under a family of transformations, including some concrete and intuitive interpretations, provide an insight on frequency distributions, graphical displays, and summary measures. The latter can then be rigorously defined, which makes it possible to construct new measures.