Spectroscopic analysis and study of nanoparticle samples is often hampered by structural diversity that presents a complex superposition of spectral signatures. By probing the spectra of small volumes within dilute samples, we can expose statistical variations in composition to obtain information unavailable from bulk spectroscopy. This new approach is demonstrated using fluorescence spectra of unsorted single-walled carbon nanotube samples to deduce structure-specific abundances and emissive efficiencies. Furthermore, correlations between intensity variations at different wavelengths provide two-dimensional covariance maps that isolate the spectra of homogeneous subpopulations. Covariance analysis is also a sensitive probe of particle aggregation. It shows that well-dispersed nanotube samples can spontaneously form loose aggregates of a type not previously recognized. Variance spectroscopy is a simple and practical technique that should find application in many nanoparticle studies.