Using measured radial velocity data from six double-lined spectroscopic binary systems PV Pup, BV Dra, AI Phe, V1130 Tau, NSV 223 (or DZ Psc), and V502 Oph, we find corresponding orbital and spectroscopic elements via the method introduced by Karami et al. (New Astron. 14, 478 (2009)). Our numerical results are in good agreement with those obtained by others using more traditional methods. Using ... [Show full abstract] a statistical analysis, we also conclude that for BV Dra, V1130 Tau, NSV 223 (or DZ Psc), and V502 Oph, a circular orbit is quite consistent.