Free Variance Calculator
Calculate population and sample variance instantly with step-by-step explanations. Essential for statistical analysis and data science.
Variance Calculator
Tip: Enter multiple values separated by commas, spaces, or semicolons
Enter at least 2 data points to calculate variance
What is Variance?
Variance is a statistical measurement that describes the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average) and thus from every other number in the set.
Variance is expressed in squared units of the original data. For example, if you're measuring heights in centimeters, the variance would be in square centimeters (cm²). This is why we often use standard deviation (the square root of variance) for easier interpretation.
Key Characteristics
- • Always non-negative (zero or positive)
- • Zero variance means all values are identical
- • Higher variance indicates greater spread in data
- • Variance is the square of standard deviation
- • More sensitive to outliers than standard deviation
Population Variance (σ²)
Where:
- σ² = population variance
- μ = population mean
- N = total number of values
- x = each individual value
Sample Variance (s²)
Where:
- s² = sample variance
- x̄ = sample mean
- n = sample size
- x = each individual value
How to Calculate Variance (Step-by-Step)
Example Dataset:
Test scores: 75, 82, 90, 85, 78, 88, 92, 80
Calculate the Mean
Subtract Mean from Each Value
Square Each Deviation
Calculate Variance
Real-World Applications of Variance
Finance & Investment
Portfolio variance measures investment risk. Higher variance indicates more volatile returns, helping investors make risk-adjusted decisions.
Quality Control
Manufacturing uses variance to monitor consistency. Low variance in product dimensions indicates reliable production processes.
Scientific Research
Variance helps determine if experimental results are statistically significant or due to random chance.
Education
Test score variance reveals class homogeneity. High variance suggests diverse student abilities requiring differentiated instruction.
Frequently Asked Questions
What's the difference between variance and standard deviation?
Standard deviation is the square root of variance. Variance is expressed in squared units, while standard deviation uses the original units, making it easier to interpret in context of your data.
Can variance be negative?
No, variance is always zero or positive because it's calculated by squaring deviations. Zero variance means all values are identical.
Why use (n-1) for sample variance?
This is Bessel's correction, which provides an unbiased estimate of population variance from sample data. Using n would systematically underestimate the true population variance.
What is a good variance value?
There's no universal "good" variance. It depends on your data context. Low variance suggests consistency, high variance indicates diversity. Compare variance relative to the mean using coefficient of variation.