  The Equal Filling Approximation, a procedure widely used in mean field
calculations to treat the dynamics of odd nuclei in a time reversal invariant
way, is justified as the consequence of a variational principle over an average
energy functional. The ideas of Statistical Quantum Mechanics are employed in
the justification. As an illustration of the method, the ground and lowest
lying states of some octupole deformed Radium isotopes are computed.
