The distribution of variation in a quantitative trait and its underlying distribution of genotypic diversity can both be shaped by stabilizing and directional selection. Understanding either distribution is important, because it determines a population’s response to natural selection. Unfortunately, existing theory makes conflicting predictions about how selection shapes these distributions, and very little pertinent experimental evidence exists. Here we study a simple genetic system, an evolving RNA enzyme (ribozyme) in which a combination of high throughput genotyping and measurement of a biochemical phenotype allow us to address this question. We show that directional selection, compared to stabilizing selection, increases the genotypic diversity of an evolving ribozyme population. In contrast, it leaves the variance in the phenotypic trait unchanged.