Standard Deviation
Standard deviation measures how spread out data values are from the mean. It is the most widely used measure of statistical variability, appearing in quality control, finance (portfolio volatility), scientific research, and machine learning. Our calculator handles both population and sample standard deviation, shows the full variance table, and visualizes the distribution.
Nombres (séparés par virgule ou espace)
Écart-type échantillon (s)
Population Std Dev (σ)
Moyenne
Variance
À propos de Standard Deviation Calculator
Standard deviation measures how spread out data values are from the mean. It is the most widely used measure of statistical variability, appearing in quality control, finance (portfolio volatility), scientific research, and machine learning. Our calculator handles both population and sample standard deviation, shows the full variance table, and visualizes the distribution.
Comment l'utiliser
- Enter your data values separated by commas or line breaks.
- Choose population (σ) or sample (s) standard deviation.
- See mean, median, variance, standard deviation, and range.
- View the frequency distribution and normal curve overlay.
Formule et méthodologie
Mean: μ = Σx / n. Population variance: σ² = Σ(x−μ)² / n. Sample variance: s² = Σ(x−μ)² / (n−1). Standard deviation = √variance. The n−1 denominator (Bessel's correction) makes the sample variance an unbiased estimator of the population variance.
Cas d'usage courants
- Finance: measuring stock volatility (higher σ = higher risk)
- Quality control: Six Sigma (process within ±3σ = 99.73% conformance)
- Academic grading: normalizing test scores to a curve
- Scientific experiments: reporting measurement uncertainty
- A/B testing: determining statistical significance of results
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