Optical robustness, uniformity, ergodicity, statistical aging, etc. dictate the applicability of nanocrystals. Based on a series of multimodal statistical analyses such as the Kolmogorov-Smirnov test, Lévy statistics, etc., we demonstrate that for CsPbBr3 perovskite nanocrystals (PNCs): (a) the extent of heterogeneity in the quality and associated physical processes is minimal; (b) the optical robustness is very high, and (c) indeed, a single PNC can depict optical behavior of its ensemble. In addition, toward prospective applications, an optically robust CsPbBr3 PNC exhibits (i) near-ergodicity and (ii) minimal statistical aging, which are extremely vital and complementary to its high defect tolerance.