Historically, statistical variance has been defined as the average of the squared differences between the previously computed variable mean under consideration and each of the values of this variable. This is the usual variance. It can be shown that the average of all the squared differences between two individual values is equal to the usual variance, as far as all the pairs of cases being compared are given the same weight. The basis of the presentation, a mathematical article published in 2017, proposes to consider an extension of variance according to the principle of not uniform but varied weights for the pairs of cases compared in the calculation. Practically, such a variability may come from the external world (for example: on a map of administrative divisions, differences between neighbouring districts can be overlooked) but it may also come from the mental interiority of subjects in a situation, more or less inclined as they may be not to take every combination of cases into consideration, or only considering some among them. The presentation will outline some extensions of this reasoning in sociology and cognitive science.
