The average color in a scene is a potentially important cue to the illuminant and thus for color constancy, but it remains unknown how well and in what ways observers can estimate the mean chromaticity. We examined this by measuring the variability in "achromatic" settings for stimuli composed of different distributions of colors with varying contrast ranges along the luminance, SvsLM, and LvsM cardinal axes. Observers adjusted the mean chromaticity of the palette to set the average to gray. Variability in the settings increased as chromatic contrast or (to a lesser extent) luminance contrast increased. Signals along the cardinal axes are relatively independent in many detection and discrimination tasks, but showed strong interference in the white estimates. This "cross-masking" and the effects of chromatic variance in general may occur because observers cannot explicitly perceive or represent the mean of a set of qualitatively different hues (e.g., that red and green hues average to gray), and thus may infer the mean only indirectly (e.g., from the relative saturation of different hues).