Population Variance Calculator
Enter numeric data assumed to represent the entire population to compute variance and standard deviation.
Mean (μ)
19.5000
Variance (σ²)
26.2500
Std. Dev. (σ)
5.1235
How to Use This Calculator
- Input all population values using spaces or commas.
- Review the computed mean, variance, and standard deviation.
- Use the results to evaluate variability across the full population.
- For sample data, use a sample variance calculator (divide by n − 1).
Formula
σ² = Σ(xi − μ)² / N
σ = √σ²
μ = Σxi / N
These formulas apply when the dataset encompasses the entire population. Use sample variance when working with samples.
Full Description
Population variance characterizes overall variability across every element in a population. It is crucial in quality control, risk analysis, and data reporting when no sampling is involved.
Frequently Asked Questions
What if my data represent a sample?
Use sample variance (divide by n − 1) for unbiased estimation. This calculator assumes a full population.
Can I include negative numbers?
Yes. Variance uses squared differences, so sign does not affect magnitude.
Why is variance always non-negative?
Because it sums squared deviations, which are always ≥ 0.
Do I need to sort the data?
No. Sorting is not required for variance calculations.