Measurements of Coulomb blockade conductance peak spacings and widths measured over large ensembles (∼10 4 peaks) of peaks in ballistic GaAs quantum dots are reported. Distributions of spacings for both broken (B≠0) and unbroken (B=0) time-reversal symmetry are roughly Gaussian with broad non-Gaussian tails and a standard deviation of 2–6% of the average spacing, comparable to the single-particle level spacing. Spacing distributions for B=0 are wider by a factor of ∼1.2±0.1 compared to B≠0, consistent with random matrix theory. Surprisingly, spacing distributions are unimodal, suggesting an absence of spin-degeneracy. Peak width distributions reflect fluctuations in the “lever arm,” or capacitance ratio η=C gate /C dot . Field-averaged peak width and spacing both change smoothly as electrons are added to the dot, but fluctuations in peak width appear uncorrelated with spacing fluctuations.