This study examines how task characteristics (the number of visual chunks and the amount of planning time) and test-taker characteristics (graph familiarity) influence the perceptual and cognitive processes involved in graph comprehension, the strategies used in describing graphs, and the scores obtained on the graph description task in a semi-direct oral test. Specifically, it investigates whether providing planning time and reducing the number of visual chunks in bar and line graphs help mitigate the influence of graph familiarity on language performance on graph description tasks. These research questions were explored using a structural equation modeling approach in a framework of the influence of the interaction between task characteristics and test-taker characteristics on task performance. It was found that graph familiarity affected the overall communicative quality of participants' performance on these graph description tasks. Graph familiarity thus represented a potential source of construct-irrelevant variance. However, reducing the number of visual chunks in a graph and providing planning time positively impacted the perceptual and cognitive processes involved in graph comprehension and helped mitigate the influence of graph familiarity. Practical and theoretical implications of this study are discussed.