The maximum values of monthly mean and smoothed monthly mean sunspot numbers in each solar cycle regarded as sets of numbers from a stochastic population are shown to conform to the general extreme value probability distribution function. Analytic expression are obtained for the two extreme value populations are derived. the statistical parameters-mode, median, mean, and standard deviation- for the populations are derived. The results are used to find the ranges of the two extremes in a group of solar cycles as a function of the number of cycles in the group. The extreme values are found to have a large dispersion compared, for example, to that found in a previous study for the largest geomagnetic storm per solar cycle as measured by the half-daily aa index. Nevertheless, the extreme scarcity of sunspots during seven solar cycles from 1634 to 1711 (the Maunder minimum) as expressed in terms of estimated annual mean sunspot numbers by Eddy is well outside the expected range of sunspot numbers for 100 solar cycles based on the cycles since then. This result suppports the argument for a change in solar cycle statistics during the Maunder minimum.