The Friedel sum rule has been derived using a grand canonical ensemble of electrons in the scattering states. The method, while illustrating the use of the statistical method of the grand canonical ensemble, clarifies the exact nature of the constraint which gives rise to this sum rule, viz. the charge neutrality of the entire crystal. An extra term has been found which cancels the contribution to the Friedel sum from the phase shifts at k = 0. This cancellation term is shown to exist in the conventional derivation if done more carefully, thus emphasizing the care needed when a finite result is sought by subtraction from two rather infinite terms. An expression for the excess charge density valid within the range of the scattering potential has been derived.