The implication of the coefficient of centrality for assessing the meaning of the mean

mean ( CV = σ μ ) . To gain a feel for how means impact the meanings of standard deviations, imagine that there are two classes and that the standard deviation of the final exam is 5 points in both of them but that the mean is 25 in Class 1 and 75 in Class 2. It follows that the coefficient of variation is 0.200 in Class 1 whereas it is 0.067 in Class 2. Thus, relative to the mean the standard deviation is thrice the size in Class 1 as in Class 2. Consequently, the actual value of the standard deviation is the same in both classes but its meaning is very different. In keeping with this Special Issue on means, my goal is not to discuss how means influence the meanings of standard deviations (see Trafimow, 2014 for this discussion). Rather, it is to show that the coefficient of variation is a two edged sword so that if means modify the meanings of standard deviations, the reverse also is so. Standard deviations influence the meanings of means. An easy demonstration involves defining a new variable, termed the coefficient of centrality (CC), which is the reciprocal of the coefficient of variation and is given as Equation (1) below.