The Mean as a Center of Equilibrium: A Torque-Based Derivation

Abstract

This work explores the mathematical relationship between the arithmetic mean from statistics and the center of equilibrium from mechanics. It demonstrates that the equilibrium condition of a system of weighted objects leads directly to the formula of the arithmetic mean. By connecting concepts from two different disciplines, this article highlights the underlying mathematical unity between statistical averaging and physical balance. The study provides a simple theoretical framework to understand how the same mathematical principle appears in both statistical analysis and mechanical equilibrium.