🎓 Mathematics • Statistics
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Variance Calculator
Computes variance s² and σ² from sums of squared deviations from the mean.
Studio-Grade Mathematical Suite
Math & Statistics Calculator
High-precision percentage, fraction arithmetic, ratio scaling, dataset averages, statistical variance, and combinatorics.
Sample Datasets:
Sample Std Dev (s)
26.4281
Population Std Dev (σ)
Sample Variance (s²)
698.447
Interquartile Range (IQR)
39.5
Count (N): 12
Sum: 605
Min: 12
Max: 92
Q1:
Q3:
What is Variance in Statistics?
Variance is the average of squared differences from the mean, measuring data spread in squared units.
Formula & Step-by-Step Calculation
s² = ∑(xᵢ - x̄)² / (n - 1)
Sample variance with Bessel’s correction.
Worked Step-by-Step Examples
Example 1
Variance of 2, 4, 6
Solution: 4
• Mean = 4, squared diffs = 4 + 0 + 4 = 8, s² = 8 / (3-1) = 4
Common Real-World & Academic Use Cases
- ✓ Statistical modeling
- ✓ Financial volatility calculations
- ✓ Quality engineering ANOVA tests
How to Use the Variance Calculator
1
Enter Numbers
Input values separated by commas.
2
Read Variance
Inspect s² and σ².
Frequently Asked Questions
Q: What is the relation between variance and standard deviation?
Standard deviation is simply the square root of variance: s = √(s²).