Standard Deviation Calculator - Free Online Variance & SD Calculator
Standard Deviation Calculator
Calculate standard deviation and variance for your dataset. Choose between population and sample calculations.
Enter Your Data
Population (σ): Use when you have data for the entire population
Sample (s): Use when you have a sample from a larger population
Results
Standard Deviation
Variance
Mean
Coefficient of Variation
Data Count
Step-by-Step Calculation
Data Distribution
How to use this calculator
📊 How to Use This Calculator
- Choose between Population (σ) or Sample (s) calculation
- Enter your data values separated by commas, spaces, or line breaks
- Click "Calculate Standard Deviation" to get results
- View standard deviation, variance, and coefficient of variation
- See step-by-step calculations and data distribution
📐 Understanding Standard Deviation
What is Standard Deviation?
Standard deviation measures how spread out numbers are from their average. A low SD means data points are close to the mean, while a high SD means they are spread out.
Population vs Sample
- Population (σ): Divide by N - use when you have all data
- Sample (s): Divide by (n-1) - use for sample data (Bessel's correction)
Variance
Variance is the square of standard deviation. It's useful in many statistical calculations but harder to interpret because units are squared.
🌟 Real-World Examples
Example 1: Test Score Consistency
Class A scores: 70, 72, 74, 76, 78 (SD = 3.16)
Class B scores: 50, 65, 74, 85, 96 (SD = 17.78)
Class A has more consistent performance.
Example 2: Manufacturing Quality
Product weights with SD = 0.5g indicate good quality control.
Product weights with SD = 5g suggest inconsistent production.
Example 3: Investment Risk
Stock A: Return = 8%, SD = 2% (low risk)
Stock B: Return = 12%, SD = 15% (high risk)
💡 Pro Tips
- • About 68% of data falls within ±1 SD from the mean
- • About 95% of data falls within ±2 SD from the mean
- • About 99.7% of data falls within ±3 SD from the mean
- • Coefficient of Variation (CV) allows comparison of SD between different scales
- • Always use sample SD unless you have the entire population
⚠️ Common Mistakes to Avoid
- • Don't forget to use (n-1) for sample standard deviation
- • Standard deviation cannot be negative
- • Don't compare SD of datasets with different units
- • Remember that SD is sensitive to outliers
- • Zero SD means all values are identical
About this calculator
Calculate standard deviation, variance, and coefficient of variation. Choose between population and sample calculations with visual distribution.
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