Standard Deviation Calculator

Calculate sample and population standard deviation with comprehensive statistical analysis

Standard Deviation Settings

Configure calculation type and input method

Use when your data is a sample from a larger population

About Standard Deviation

Sample vs Population

  • Sample (n-1): Use when data is a sample from a larger population
  • Population (n): Use when data represents the complete population
  • Sample standard deviation is typically larger than population

Interpretation

  • Low Std Dev: Data points are close to the mean
  • High Std Dev: Data points are spread out from the mean
  • 68-95-99.7 Rule: Normal distribution percentages

Key Formulas

  • Sample: σ = √[Σ(x - μ)² / (n-1)]
  • Population: σ = √[Σ(x - μ)² / n]
  • Variance: σ² (square of standard deviation)

Uses

  • Quality control and process improvement
  • Risk assessment in finance
  • Research and data analysis
  • Performance measurement