Implicit in our description of central tendency is the idea that even as one speaks
of some stable component, one acknowledges the fundamental variability inherent in
that process and thus its probabilistic nature. Because of this, we claim that the
notion of an average understood as a central tendency is inseparable from the notion
of spread. That average and variability are inseparable concepts is clear from the
fact that most people would consider talking about the average of a set of identical
values to be odd. In addition, it is hard to think about why a particular measure of
center makes sense without thinking about its relation to the values in the
distribution (e.g., the mean as the balance point around which the sum of the
deviation scores is zero, or the median as the point where the number of values
above equals the number of values below).