Uncertainty is an important and fundamental concept in physics education. Students are often first exposed to uncertainty in introductory labs, expand their knowledge across lab courses, and then are introduced to quantum mechanical uncertainty in upper-division courses. This study is part of a larger project evaluating student thinking about uncertainty across these contexts. In this research, we investigate advanced physics student thinking about uncertainty by asking them conceptual questions about how a hypothetical distribution of measurements would change if "more"or "better"data were collected in four different experimental scenarios. The scenarios include both classical and quantum experiments, as well as experiments that theoretically result in an expected single value or an expected distribution. This investigation is motivated by our goal of finding insights into students' potential point- and setlike thinking about uncertainty and of shining light on the limitations of those binary paradigms. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.