This study examined whether graph schemas are based on perceptual features (i.e., each graph has its own graph schema) or common invariant structures (i.e., graphs share several common schemas), as well as which graph type (bar, line, or pie) is optimal for comparing discrete groups. The mixing-costs paradigm was used in three experiments. Two graphs were examined at a time (Experiment 1: bar vs. line, Experiment 2: bar vs. pie, Experiment 3: line vs. pie). Participants were presented graphs containing quantities for three groups in pure and mixed blocks and asked to constantly compare two groups. The results showed that graph schemas are built on a common invariant structure. Mixing costs were displayed by pairing pie charts to either bar or line graphs. Bars had no mixing cost when paired with lines. Bars were the quickest to compare groups compared to lines and pies. Furthermore, adjacent groups were processed quicker than non-adjacent groups. Across experiments analyses showed tentative evidence for the hierarchical view of graph schema.