Statistical theory serve as the foundation for understanding and interpreting data across various disciplines? Explore its role in probability theory, hypothesis testing, regression analysis, and sampling techniques. Discuss key concepts such as probability distributions, central limit theorem, confidence intervals, and p-values, elucidating their significance in making informed decisions and drawing valid conclusions from data. Additionally, delve into the practical applications of statistical theory in fields like economics, biology, psychology, and sociology, highlighting its ability to uncover patterns, relationships, and trends, thereby aiding in prediction, inference, and decision-making processes.