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:

- It’s more intuitive: if we want to mesure the regularity, the homogeneity of a sample, then I think that it’s more intituitive to calculate the mean of the diferences between mean and the values of the sample instead of calculate the square root of those differences squared. All my students say “Why squared?”
- We don’t need standard deviation until high courses. For examples if we teach gaussian distribution, confidence intervals or linear regression. But if we introduce statistics or if we want to analyze data samples, I think we need simple deviation parameter
^{1}

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.

A range of the sample could be another one↩