Reasoning over plots by question answering (QA) is a challenging machine learning task at the intersection of vision, language processing, and reasoning. Existing synthetic datasets (FigureQA, DVQA) do not model variability in data labels, real-valued data, or complex reasoning questions. Consequently, proposed models for these datasets do not fully address the challenge of reasoning over plots. We propose PlotQA with 8.1 million question-answer pairs over 220,000 plots with data from real-world sources and questions based on crowd-sourced question templates. 26% of the questions in PlotQA have answers that are not in a fixed vocabulary, requiring reasoning capabilities. Analysis of existing models on PlotQA reveals that a hybrid model is required: Specific questions are answered better by choosing the answer from a fixed vocabulary or by extracting it from a predicted bounding box in the plot, while other questions are answered with a table question-answering engine which is fed with a structured table extracted by visual element detection. For the latter, we propose the VOES pipeline and combine it with SAN-VQA to form a hybrid model SAN-VOES. On the DVQA dataset, SAN-VOES model has an accuracy of 58%, significantly improving on highest reported accuracy of 46%. On the PlotQA dataset, SAN-VOES has an accuracy of 54%, which is the highest amongst all the models we trained. Analysis of each module in the VOES pipeline reveals that further improvement in accuracy requires more accurate visual element detection.