Variance Calculator : Calculate Sample (s²) & Population (σ²) Variance

The Calcivo Variance Calculator computes the statistical variance for any dataset. It calculates the average of squared differences from the mean, providing both Sample Variance (s²) and Population Variance (σ²).

Interactive Calculator

100% Client-Side Engine

Sample Variance (s² = SS / (n - 1))

3.5

Population Variance (σ² = SS / N)

2.9167

Arithmetic Mean (x̄)

5.5

Observations Count (N)

6

Sum of Squared Deviations (SS)

17.5

Variance Derivation Steps

1. Arithmetic Mean: x̄ = 33 ÷ 6 = 5.5

2. Sum of Squared Differences (SS): 17.5

3. Population Variance σ² = SS / N = 17.5 / 6 = 2.9167

4. Sample Variance s² = SS / (n - 1) = 17.5 / (6 - 1) = 3.5

Step-by-Step Examples

Variance of 6 Numbers

Values: 4, 8, 6, 5, 3, 7.

Inputs: Values: 4, 8, 6, 5, 3, 7

Result: Sample s² = 3.5000, Pop σ² = 2.9167 (Mean = 5.50)

Mean = 5.5. SS = 17.5. s² = 17.5 / 5 = 3.5. σ² = 17.5 / 6 = 2.9167.

How to Use This Tool

Enter dataset numbers separated by commas or spaces.
Click Calculate.
Review sample variance, population variance, and Sum of Squares (SS).

Frequently Asked Questions

Standard deviation is the positive square root of variance (SD = √Variance). Conversely, variance is standard deviation squared.

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