Standard Deviation Solver

Standard deviation (σ or s) is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. Mathematical Formulas: • Population: σ = √[Σ(xi - μ)² / N] • Sample: s = √[Σ(xi - x̄)² / (n-1)] Where: • xi = individual data points • μ = population mean, x̄ = sample mean • N = population size, n = sample size Key Characteristics: 1. Always non-negative (≥ 0) 2. Zero means no variation 3. Same units as original data 4. Sensitive to outliers Interpretation: • Low σ: Data points cluster near mean • High σ: Data widely spread from mean • Empirical Rule (68-95-99.7): ~68% within ±1σ, ~95% within ±2σ, ~99.7% within ±3σ Applications: Quality control, risk assessment, research, financial analysis, and understanding data variability.