Standard Deviation Calculator
Calculate mean, variance, and standard deviation of a dataset
What is Standard Deviation?
Standard deviation (σ) is a measure of how spread out numbers are from their average (mean). A low standard deviation means data points are close to the mean, while a high standard deviation means data is more spread out.
Step-by-Step Calculation
Visual Distribution
Practical Applications
- • Measure stock volatility
- • Assess investment risk
- • Portfolio analysis
- • Market trend evaluation
- • Manufacturing consistency
- • Process improvement
- • Defect rate analysis
- • Performance metrics
- • Test score analysis
- • Research data evaluation
- • Survey result interpretation
- • Performance comparisons
- • Athlete performance tracking
- • Health metrics monitoring
- • Training consistency
- • Clinical trial analysis
Real-World Examples
Stock A: Returns = [2%, 3%, 2.5%, 3.5%, 2%] → σ = 0.6% (Low volatility)
Stock B: Returns = [-5%, 10%, -2%, 8%, -4%] → σ = 6.5% (High volatility)
Lower σ = More stable, Higher σ = More risky
Class A: Scores = [85, 87, 86, 88, 84] → σ = 1.5 (Consistent performance)
Class B: Scores = [60, 95, 70, 90, 75] → σ = 13.2 (Varied performance)
Lower σ = Students performing similarly
Machine A: Part lengths = [10.1, 10.0, 10.1, 9.9, 10.0] mm → σ = 0.08mm
Machine B: Part lengths = [9.5, 10.5, 9.8, 10.3, 9.9] mm → σ = 0.38mm
Machine A produces more consistent parts
Interpreting Standard Deviation
- • 68% of data falls within 1σ of the mean
- • 95% of data falls within 2σ of the mean
- • 99.7% of data falls within 3σ of the mean
💡 Quick Tips
- ▸Sample vs Population: This calculator uses population standard deviation (divides by n)
- ▸Outliers: Extreme values significantly increase standard deviation
- ▸Zero σ: Means all values are identical
- ▸Units: Standard deviation has the same units as your original data