law of large numbers
a mathematical principle indicating that as the sample size increases, the theoretical expectations of its statistical properties will be more and more closely realized. For example, as the number of replications of an experiment increases, the average (mean) of the observed results will approach the true average (theoretical probability in the population) with increasing accuracy. According to the strong law of large numbers, the average of the results obtained from a large number of trials will converge upon the theoretically expected value, becoming closer as more trials are performed. In distinction, the weak law of large numbers states that the average is likely to converge upon the expected value as more trials are conducted. Thus, the essential difference between the two laws is that the former insists on convergence whereas the latter expects convergence.