Variance Calculator
Calculate statistical variance (σ²) for numeric datasets.
GCD & LCM Calculator
About Variance Calculator
The Statistical Variance & Standard Deviation Calculator computes Sample Variance ($s^2$), Population Variance ($\sigma^2$), Standard Deviation ($s, \sigma$), Mean ($\mu, \bar{x}$), Sum of Squares ($SS$), and Coefficient of Variation ($CV$) with step-by-step deviation tables.
How to Use Variance Calculator
Step 1
Enter your data numbers separated by commas, spaces, or newlines.
Step 2
Select Sample ($n-1$) or Population ($N$) mode.
Step 3
Review the step-by-step deviation calculations.
Step 4
Click "Copy Statistical Report".
Practical Use Cases for Variance Calculator
Financial Volatility & Portfolio Risk Analysis
Measure the historical return volatility and standard deviation of stock portfolios to calculate Sharpe ratios.
Scientific Experiment & Quality Control Variance
Evaluate measurement consistency and manufacturing tolerance deviations across sample batches.
Input & Output Examples
Calculating Variance for Dataset [10, 12, 23, 23, 16, 23, 21, 16]
Dataset: 10, 12, 23, 23, 16, 23, 21, 16
Mean = 18.0 | Sample Variance ($s^2$) = 27.43 | Sample Std Dev ($s$) = 5.24 | Population Variance ($\\sigma^2$) = 24.00
Key Features & Performance
- ✓Calculates both Sample ($n-1$ Bessel correction) and Population ($N$) variance & standard deviation.
- ✓Displays full step-by-step deviation table ($x_i - \\bar{x}$ and $(x_i - \\bar{x})^2$).
- ✓Calculates Mean, Median, Range, Sum of Squares ($SS$), and Coefficient of Variation ($CV$).
- ✓100% Client-Side calculation.
- ✓1-Click Copy full statistical report.
Key Terminology & Definitions
Sample Variance ($s^2$)
$s^2 = \\frac{\\sum (x_i - \\bar{x})^2}{n - 1}$, using Bessel's correction ($n-1$) to eliminate bias when estimating population variance from a sample.
Standard Deviation ($\\sigma, s$)
The square root of variance, measuring the typical distance between data points and the mean in original measurement units.