Although a traditionally Italian research topic, the subject of descriptive statistics has received renewed attention at an international level, owing to the need for a more precise charac terization of the main classes of descriptive statistics, both for application as summaries of distributions and in relation to non-parametric models and robust procedures. This paper endeavours to establish generally acceptable definitions of variability, spread, dispersion, together with their most important implications, especially concerning the construction of indexes or measures. Notwithstanding that general properties (for random variables) comprise all cases of observed distributions, some non-intuitive results will be shown concerning comparisons of statistical distributions and of some well known variability measures computed on them.