📉 Variance Calculator

Variance

What is Variance?

Variance measures how far each number in a dataset is from the mean. It is the square of the standard deviation. Variance gives more weight to outliers because differences are squared.

Population Variance σ² = Σ(xᵢ − μ)² / N
Sample Variance s² = Σ(xᵢ − x̄)² / (N−1)

Variance vs Standard Deviation

  • Variance = Standard Deviation²
  • Variance is in squared units; SD is in original units
  • SD is more interpretable; variance is used in calculations

Frequently Asked Questions

What is the variance of 2, 4, 6? ▼
Mean = 4. Deviations: (2−4)²=4, (4−4)²=0, (6−4)²=4. Population variance = (4+0+4)/3 = 2.67. Sample variance = (4+0+4)/2 = 4.
Can variance be negative? ▼
No. Variance is always zero or positive because it is the average of squared differences. Variance equals zero only when all values in the dataset are identical.
Why do we square differences in variance? ▼
Squaring ensures all deviations are positive (so negatives and positives don't cancel out) and gives more weight to larger deviations.