We examine the effects of extreme price values on the Fisher and Tornqvist price index formulas. After a brief overview of basic price index theory, we use a simple model to consider the impact of outliers on the unweighted arithmetic, harmonic, and geometric means of a collection of values. Then, under the same model, we investigate the effect of a single extremely high or low price on the price index formulas, which involve weighted versions of these means. Further investigation using Taylor series approximations leads to some general conclusions regarding the relative robustness of the Fisher and Tornqvist indexes. We illustrate these conclusions with empirical results based on airfare data from the Department of Transportation's Passenger Origin and Destination Survey.