Discussed are physical implications of two sets of moments 〈 s n 〉 and 〈 t n 〉 associated with the electron-pair radial sum S ( s ) and difference T ( t ) densities. The first moments 〈 s 〉 and 〈 | t | 〉 are equivalent to the sum 〈 r > 〉 + 〈 r < 〉 and the difference 〈 r > 〉 - 〈 r < 〉 of the inner 〈 r < 〉 and outer 〈 r > 〉 radii, respectively. The variances σ s 2 = 〈 s 2 〉 - 〈 s 〉 2 and σ t 2 = 〈 t 2 〉 - 〈 t 〉 2 of S ( s ) and T ( t ) are found to be connected with the statistical radial correlation coefficient τ [ r ] in a straightforward manner. For the 53 atoms He through Xe in their ground states and for some singly-excited states of the He atom, the first and second moments as well as the radial correlation coefficient are systematically studied at the Hartree–Fock limit level. The effect of electron correlations is also examined for the He atom and its isoelectronic ions.