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We report experiments on the equipartition of kinetic energy in a mixture of pairs of different types of grains vibrated in two dimensions. In general, the two types of grains do not attain the same granular temperature, T g= 1/2 m< v 2>. However, the temperature ratio is constant in the bulk of the system and independent of the vibration velocity. The ratio depends strongly on the ratio of mass densities of the grains, but not on their inelasticity. Also, the temperature ratio is insensitive to compositional variables such as the number fraction of each component and the total number density. We conclude that a single granular temperature, as traditionally defined, does not characterize a multicomponent mixture.