Question-asking is a necessary step towards formulating hypotheses, making decisions, and solving problems, and is Practice #1 in the Next Generation Science Standards. To improve question-asking, educators and researchers need a way to categorize and evaluate students' questions, so as to judge whether an intervention has been effective. We collected a corpus of questions generated by undergraduates as they explored data pertaining to sea level and climate. To capture a broad range of questions, we recruited participants from all majors and multiple institutions, used different prompts to elicit questions, showed both physical- and social-science data, and presented the data both on paper and interactively. We developed a taxonomy of question types informed by geoscientific habits of mind and designed to be applicable across a wide range of data types. We assigned Bloom's cognitive levels to each question type, and developed a quality metric for question sets. There were wide individual differences in both quality and quantity of questions, plus some systematic differences by experimental condition. Prompting to ask as many questions as possible elicited more high level questions overall, but prompting to write questions you would like to ask the scientist elicited important questions about how the data were collected. Encouragingly, over 70% of participants generated at least one question at the highest Bloom's level. Implications for instruction include that assigned question-asking can be an opportunity to engage all students in question asking, and that students can ask good questions about complex data before the data are explained to them.