Mean value estimate errors for estuarine (and oceanic) parameters which exhibit serial correlation and nonstationarity over a finite record length are discussed. It is shown that when trends are nonlinear over the record length, the mean value estimate error does not decrease with time. Instead, it goes through a minimum and then increases again. An optimal averaging time over which the mean estimate error is minimum is presented. The mean circulation in the lower St. Lawrence estuary is described over a record length of 78.5 days in 1979. Standard, bias, and rms errors in mean value estimates are discussed, and an averaging time yielding a minimum error is suggested for the lower St. Lawrence estuary. New measured features of the mean circulation are: a coastal current flowing downstream near the north shore which deflects to the right at the mouth, and a 2 cm/s inflow in the bottom layer at mid-channel location.