A Monte Carlo approach is employed to estimate the distribution of an equivalent conductivity measure, the block conductivity, which characterizes the total flow rate through a two-dimensional bounded domain and which is itself a random variable. Chi-square goodness-of-fit tests indicate that the lognormal distribution is an appropriate choice for the block conductivity distribution. For square domains, the mean and variance of the block conductivity are seen to be closely approximated using the statistics of local averages of log conductivity. ¿ American Geophysical Union 1993