  Colouring the vertices of a graph $G$ according to certain conditions can be
considered as a random experiment and a discrete random variable $X$ can be
defined as the number of vertices having a particular colour in the proper
colouring of $G$. In this paper, we extend the concepts of mean and variance,
two important statistical measures, to the theory of graph colouring and
determine the values of these parameters for a number of standard graphs.
