Stevens's power law ([Psi][infinity][Phi][beta]) captures the relationship between physical ([Phi]) and perceived ([Psi]) magnitude for many stimulus continua (e.g., luminance and brightness, weight and heaviness, area and size). The exponent ([beta]) indicates whether perceptual magnitude grows more slowly than physical magnitude ([beta] less than 1), directly as physical magnitude ([beta] [is isomorphic to] 1), or more quickly than physical magnitude ([beta] greater than 1). These exponents are typically determined using judgments of single stimuli. Miller and Sheldon (1969) found that the validity of Stevens's Power Law could be extended to the case where the mean of a property in an ensemble of items was judged (i.e., average length or average tilt where [beta] [is isomorphic to] 1). The present experiments investigate the extension of this finding to perceived brightness with [beta] [is isomorphic to] 0.33 and find evidence consistent with predictions made by Miller and Sheldon. (Contains 3 figures and 2 tables.)