Connections between Statistics and Mathematics/Probability

Michael A. Proschan and Pamela A. Shaw

The American Statistician, 2025, vol. 79, issue 3, 410-415

Abstract: There are many connections between probability, other mathematics courses, and statistics. Understanding these connections provides insights that might not be fully appreciated when considering each discipline in isolation. While the typical instruction of statistics courses relies on elucidating its foundational principles from mathematical and probability theory, it is generally less appreciated that statistics can in turn provide a deeper understanding of results in mathematics and probability. We offer several examples for which knowledge of statistics can shed new light on probability and other mathematics results. Examples span both undergraduate and graduate level material. In today’s data driven-world, many students are naturally curious about statistics and are exposed to this field early in their undergraduate curriculum. Leveraging connections between statistics and mathematics and probability makes theoretical concepts more intuitive and relevant, fostering a better understanding.

Date: 2025
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DOI: 10.1080/00031305.2025.2453230

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