Standard Deviation Calculator

Calculate standard deviation, variance, mean, median, and other statistics with step-by-step solutions and visualizations.

Calculator

Sample uses (n-1), Population uses n

Enter numbers separated by commas, spaces, or newlines to calculate standard deviation and other statistics.

Complete User Guide

What is Standard Deviation?

Standard deviation measures the spread or dispersion of data points around the mean. A low standard deviation indicates data points are close to the mean, while a high standard deviation indicates data points are spread out.

Sample vs Population

  • Sample Standard Deviation: Uses (n-1) in denominator. Use when data is a sample from a larger population.
  • Population Standard Deviation: Uses n in denominator. Use when data represents the entire population.

Formulas

  • Sample SD: s = √[Σ(x - x̄)² / (n-1)]
  • Population SD: σ = √[Σ(x - μ)² / n]
  • Variance: Square of standard deviation

Examples

Example 1: Sample Data

Input: 10, 20, 30, 40, 50

Mean: 30

Sample SD: ≈ 15.81

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