Historically, two important approaches to the concept of electronegativity have been in terms of: (a) an atom in a molecule (e.g., Pauling) and (b) the chemical potential. An approximate form of the latter is now widely used for this purpose, although it includes a number of deviations from chemical experience. More recently, Allen introduced an atomic electronegativity scale based upon the spectroscopic average ionization energies of the valence electrons. This has gained considerable acceptance. However it does not take into account the interpenetration of valence and low-lying subshells, and it also involves some ambiguity in enumerating d valence electrons. In this paper, we analyze and characterize a formulation of relative atomic electronegativities that is conceptually the same as Allen's but avoids the aforementioned problems. It involves the property known as the average local ionization energy, I̅(r), defined as [Formula: see text], where ρi(r) is the electronic density of the i(th) orbital, having energy εi, and ρ(r) is the total electronic density. I̅(r) is interpreted as the average energy required to remove an electron at the point r. When I̅(r) is averaged over the outer surfaces of atoms, taken to be the 0.001 au contours of their electronic densities, a chemically meaningful scale of relative atomic electronegativities is obtained. Since the summation giving I̅(r) is over all occupied orbitals, the issues of subshell interpenetration and enumeration of valence electrons do not arise. The procedure is purely computational, and all of the atoms are treated in the same straightforward manner. The results of several different Hartree-Fock and density functional methods are compared and evaluated; those produced by the Perdew-Burke-Ernzerhof functional are chemically the most realistic.