In the nano-aerosol mass spectrometer, individual particles in the 10-30 nm size range are trapped and irradiated with a high pulse energy laser beam. The laser pulse generates a plasma that disintegrates the particle into atomic ions, from which the elemental composition is determined. Particle-to-particle variations among the mass spectra are shown to arise from plasma energetics: Low ionization energy species are enhanced in some spectra while high ionization energy species are enhanced in others. These variations also limit the accuracy and precision of elemental analysis, with higher deviations generally observed when low ionization energy species are dominant in the mass spectrum. For standard datasets generated from nominally identical particles, it is shown that that the error associated with composition measurement is random and that averaging the spectra from a few tens of particles is sufficient for measuring the mole fractions of common elements to within about 10% of the expected value. Averaging a greater number of particles offers limited improvement of the measurement precision but has the deleterious effect of degrading the measurement time-resolution, which is given by the time needed to obtain the required number of particle spectra for averaging. An internally mixed ambient particle dataset was found to give a similar result to the standard datasets, that is, the measured elemental composition converged to the average value after a few tens of particles were averaged.