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I do not teach standard deviation (I teach mean deviation instead)

Authors
Xavier Bordoy
Date of creation

Abstract

Why we have to teach standard deviation?

Legally, I have to teach standard deviation \(\sigma\) (Conselleria d’Educació i Cultura de les Illes Balears 2009). But really I have to teach standard deviation? In low levels of secondary education I do not teach it. I teach mean deviation, \(d_m\). Why:

The only disadvantage I think we would have if we teached the \(d_m\) instead of \(\sigma\) is that we could not take the most references in scientific literature, which use \(\sigma\). I thought about it many times. And I think that the reason, the real reason, for which mathematicians use \(\sigma\) instead \(d_m\) is because, as a function, \(\sigma\) it’s derivable and \(d_m\) is not. So it allows getting easy bounds with known distributions (like gaussian ones).

References

Conselleria d’Educació i Cultura de les Illes Balears. 2009. “Ordre de La Consellera d’Educació I Cultura de 22 de Juliol de 2009, Per La Qual S’estableix El Currículum de L’educació Secundària Per a Persones Adultes Que Condueix a L’obtenció Del Títol de Graduat En Educació Secundària Obligatòria a Les Illes Balears.” http://www.caib.es/eboibfront/pdf/VisPdf?action=VisHistoric&p_any=2009&p_numero=117&p_finpag=55&p_inipag=4&idDocument=629435&lang=ca.


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