Geometric mean G.M. = (x₁ × x₂ × ... × xₙ)^(1/n) = nth root of product. Also G.M. = antilog[Σ(log xi)/n]. For grouped data: G.M. = (x₁^f₁ × x₂^f₂ × ...)^(1/n). Applications: Growth rates, average percentages, financial returns. Example: Returns 10%, 20%, 5%. G.M. = (1.10 × 1.20 × 1.05)^(1/3) = (1.386)^(1/3) ≈ 1.1149 or 11.49%. Solving: Use logarithms to avoid large numbers. For two values: G.M. = √(x₁ × x₂). Advantage: Better for rates and ratios. Disadvantage: Cannot handle zero/negative values. Exam tip: Use for growth problems, average rates. G.M. ≤ A.M. (equality if all values same).