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Small perturbations in the structure of materials significantly affect their properties. One example is single wall carbon nanotubes (SWCNTs), which exhibit chirality-dependent near-infrared (NIR) fluorescence. They can be modified with quantum defects through the reaction with diazonium salts, and the number or distribution of these defects determines their photophysics. However, the presence of multiple chiralities in typical SWCNT samples complicates the identification of defect-related emission features. Here, we show that quantum defects do not affect aqueous two-phase extraction (ATPE) of different SWCNT chiralities into different phases, which suggests low numbers of defects. For bulk samples, the bandgap emission (E11) of monochiral (6,5)-SWCNTs decreases, and the defect-related emission feature (E11*) increases with diazonium salt concentration and represents a proxy for the defect number. The high purity of monochiral samples from ATPE allows us to image NIR fluorescence contributions (E11= 986 nm and E11* = 1140 nm) on the single SWCNT level. Interestingly, we observe a stochastic (Poisson) distribution of quantum defects. SWCNTs have most likely one to three defects (for low to high (bulk) quantum defect densities). Additionally, we verify this number by following single reaction events that appear as discrete steps in the temporal fluorescence traces. We thereby count single reactions via NIR imaging and demonstrate that stochasticity plays a crucial role in the optical properties of SWCNTs. These results show that there can be a large discrepancy between ensemble and single particle experiments/properties of nanomaterials.