In this talk we attempt to rigorize the notion of Pearson's skewness. Informally, a probability distribution is positively skewed if its left tail is "spreading short" and its right tail is "spreading longer", and negatively skewed if vice versa. We use metric space centroids (i.e., Frechet means) to define generalized notions of positive and negative skewness that we call truly positive and truly negative. We apply the probabilistic methods of coupling and stochastic dominance for determining whether a continuous random variable is truly positively skewed. We present some basic examples of true positive skewness, thus demonstrating how the approach works in general.