Ensemble encoding supports the rapid extraction of visual statistics about distributed visual information. Researchers typically study this ability with the goal of drawing conclusions about how such encoding extracts information from natural scenes. Here we argue that a second domain can serve as another strong inspiration for understanding ensemble encoding: graphs, maps, and other visual presentations of data. Data visualizations allow observers to leverage their ability to perform visual ensemble statistics on distributions of spatial or featural visual information to estimate actual statistics on data. We survey the types of visual statistical tasks that occur within data visualizations across everyday examples, such as scatterplots, and more specialized images, such as weather maps or depictions of patterns in text. We divide these tasks into four categories: identification of sets of values, summarization across those values, segmentation of collections, and estimation of structure. We point to unanswered questions for each category and give examples of such cross-pollination in the current literature. Increased collaboration between the data visualization and perceptual psychology research communities can inspire new solutions to challenges in visualization while simultaneously exposing unsolved problems in perception research.