How do university students understand the graphs that they read in their textbooks? How does their knowledge regarding the content and their statistical training influence this understanding? Does the kind of task demand also influence this understanding? To answer these questions, we asked a group of psychology students and a group of economics students to choose the most suitable graph for presenting the results of different psychological research studies (reports) (selection task) or to explain in words the results of the same reports shown by means of their graphic representations only (interpretation task). The results showed there were very few differences between groups. Most of the students were able to relate textual information to the adequate graph, but also revealed significant shortcomings and mistakes in their understanding of important syntactic aspects of graphs. They also interpreted the graphs correctly but their interpretation had different levels of complexity, which were not always optimal. We also identified significant differences regarding the difficulty of the reports and the kinds of misinterpretations of graphs. The two tasks thus revealed different pictures of students' skills in reading and interpreting graphs and, consequently, how the characteristics of task demands influence their performance.