Variance Calculator

Calculate population and sample variance with detailed statistical analysis

Population Variance

0 σ² (sigma squared)
0 Mean (μ)
0 Standard Deviation (σ)
Count: 0
Sum: 0
Sum of Squared Deviations: 0

Sample Variance

0 s²
0 Mean (x̄)
0 Standard Deviation (s)
Count: 0
Sum: 0
Degrees of Freedom: 0

How to Use the Variance Calculator

Our comprehensive variance calculator provides two calculation modes for precise statistical analysis:

📊 Population Variance

Use when you have data for the entire population. The formula divides by N (total count) and uses the symbol σ² (sigma squared). Perfect for complete datasets where you want to measure the variability of all values.

📈 Sample Variance

Use when your data represents a sample from a larger population. The formula divides by N-1 (degrees of freedom) and uses the symbol s². This provides an unbiased estimate of population variance.

Variance measures how much the data points vary from the mean. A higher variance indicates more spread in the data, while a lower variance indicates data points are closer to the mean. Our variance tool also calculates related statistics like mean and standard deviation.

Frequently Asked Questions

What is the difference between variance and standard deviation?
Variance is the average of squared differences from the mean, while standard deviation is the square root of variance. Standard deviation is in the same units as your original data, making it easier to interpret.
When should I use population vs sample variance?
Use population variance when you have data for the entire population. Use sample variance when your data represents a sample from a larger population that you want to make inferences about.
What does a high variance indicate?
High variance indicates that data points are spread out widely from the mean, showing high variability. Low variance indicates data points are clustered close to the mean, showing consistency.
How do I interpret variance results?
Variance is always positive and is measured in squared units of your original data. For easier interpretation, look at the standard deviation, which is in the same units as your original data.