From Uncertainty to Insight: The Fundamental Value of Probability Theory and Mathematical Statistics in the Era of Big Data_Vol. 4 No. 3 (JBDC 2026)_Journal of Big Data and Computing (ISSN: 2959-0590)

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From Uncertainty to Insight: The Fundamental Value of Probability Theory and Mathematical Statistics in the Era of Big Data

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DOI: https://doi.org/10.62517/jbdc.202601312

Author(s)

Yuqi Zhu

Affiliation(s)

Zhejiang Hangzhou No.4 High School International School, Hangzhou, Zhejiang, China

Abstract

The defining feature of the big data era is not simply "massive data volume," but a fundamental shift in data dimensions: high volume, variety, velocity, and low value density. Against this background, the foundational value of probability theory and mathematical statistics has become increasingly prominent-the former provides a rigorous mathematical framework for uncertainty, while the latter offers systematic methods for extracting regularities from data. Based on the knowledge foundation of high school students, this paper systematically reviews the core concepts of probability theory and mathematical statistics and their deep connections with big data, analyzes their foundational value in fields such as prediction, decision-making, algorithms, quality control, and causal analysis, and illustrates them through three real-life cases: recommendation systems, epidemic forecasting, and learning analytics. The study shows that the relationship among the three can be aptly compared to "a building, its foundation, and its superstructure": probability theory is the theoretical foundation, mathematical statistics is the methodological bridge, and big data is the frontier of application. On this basis, the paper further discusses the implications for high school mathematics education: dispelling the myth that "mathematics is useless," cultivating statistical thinking and data awareness, and laying the groundwork for data literacy in the age of intelligence.

Keywords

Probability Theory; Mathematical Statistics; Big Data; Statistical Thinking; Data Literacy

References

[1] Zhang Wei, Liu Ming. Analysis of the Application of Probability Theory and Mathematical Statistics in Data Mining [J]. Science & Technology Information, 2024(06). [2] Gao Song. Expert Perspective: Quality Management and Probabilistic Thinking under Big Data [EB/OL]. InfinityQS, 2025-04-25. [3] Wanshi. Programmer’s Mathematics (XIII): Mathematical Thinking in Data Processing and Analysis [EB/OL]. Huawei Cloud Community, 2025-12-21. [4] Li Qiang. How to Cultivate Students' Data Analysis Literacy [N]. China Education Daily, 2025-09-22(05). [5] Liu Jun. Thoughts on the Implementation of Artificial Intelligence-Viewing AI from Statistics [R]. Department of Statistics and Data Science, Tsinghua University, 2026. [6] Chen Hao, Zhao Lei. The Full Process of Econometric Multi-Source Data Processing, Machine Learning Prediction, and Complex Causal Identification [EB/OL]. ScienceNet.cn, 2026-01-15. [7] Han Jiawei, Micheline Kamber. Data Mining: Concepts and Techniques [M]. 3rd ed. Morgan Kaufmann, 2011. [8] Pearl, Judea. Causality: Models, Reasoning, and Inference [M]. 2nd ed. Cambridge University Press, 2009. [9] Wu Xiaoling. Research on the Application of Big Data Analysis Based on Probability Statistics [J]. Journal of Mathematics and Statistics, 2023(12). [10] Breiman, Leo. Statistical Modeling: The Two Cultures [J]. Statistical Science, 2001, 16(3): 199-215.