In this paper a new framework for the study of measures of dispersion for a class of $n$-dimensional lists is proposed. The concept of monotonicity with respect to a "sharpened"-type order is introduced. This type of monotonicity, together with other well known conditions, allows to create a reasonable and general ambit where the notion of dispersion measure can be studied. Some properties are analized and relations with other approaches carried out by different authors on this subject are established.