Both graph comprehension and data analysis and interpretation are influenced by one's prior knowledge and experiences. To understand how one's prior knowledge and experiences interact with their analysis of a graph, we conducted think-aloud interviews with general chemistry students as they interpreted a graph to determine optimal conditions for an experiment. Afterwards, students engaged in a simulated peer review by reviewing three sample responses, which further revealed their reasoning. We deconstructed students' analyses using Data-Frame Theory to identify the prior knowledge and experiences that informed and guided their analysis, as well as characterizing moments in which their analysis was influenced by different sources of information. Using template analysis, we present and discuss four themes: establishing the frame, observing and interacting with the data, data-frame interactions, and when frames change. From these findings, we discuss implications for utilizing students' prior knowledge and experiences to aid in their data analysis and interpretation, as well as identify opportunities for future research.