The variances of the fission fragment mass distributions for the symmetric case, over a wide range of the fissility of the compound nucleus have been investigated within the framework of random neck rupture model (RNRM) proposed by Brosa et al. The shape of the fissioning nucleus is generated excluding crel (i.e. c$_rel$ = 1) in the RNRM model, which results in more continuous shape of fissioning nucleus at boundaries connecting heads toneck in the scission shape. This shape-modified RNRM model has been used to analyse experimental data of mass variances for symmetric mass distributions of 27 systems in a wide region of fissility (0.7–0.95). The average totalkinetic energies, $\langleTKE\rangle$s, for these fissioning systems have been taken from Viola systematics. The neck radius is an important parameter of the RNRM model and this has been varied to fit the experimental mass variances data.The systematics of the resulting neck radii are studied as a function of fissility and nuclear potential through γ0, the surface energy coefficient. It is found that the neck radii that fit the experimentally observed variances of the massdistributions fall into two groups. Empirical formulae have been obtained for the neck radii for these two groups of fissioning systems. Usage of the empirical formulae for neck radii predict the mass variances reasonably wellfor five test systems and it is shown that these predictions of the neck radii are better than the predictions with the Rayleigh criterion.