Different graph types might differ in group comparison due to differences in underlying graph schemas. Thus, this study examined whether graph schemas are based on perceptual features (i.e., each graph has a specific schema) or common invariant structures (i.e., graphs share several common schemas), and which graphic type (bar vs. dot vs. tally) is the best to compare discrete groups. Three experiments were conducted using the mixing-costs paradigm. Participants received graphs with quantities for three groups in randomized positions and were given the task of comparing two groups. The results suggested that graph schemas are based on a common invariant structure. Tally charts mixed either with bar graphs or with dot graphs showed mixing costs. Yet, bar and dot graphs showed no mixing costs when paired together. Tally charts were the more efficient format for group comparison compared to bar graphs. Moreover, processing time increased when the position difference of compared groups was increased.