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Math Calculator

Variance Calculator.

Variance (sample)
22.266667
Count (n)6
Mean18.666667
Standard Deviation4.718757
Sum of Squares (SS)111.333333

Parsed 6 values: 12, 15, 18, 20, 22, 25

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What Is a Variance Calculator?

Variance measures how spread out a set of numbers is around the mean. This free variance calculator computes population or sample variance, standard deviation, mean, count, and sum of squares from any pasted list.

How to Use This Calculator

  1. Choose Population (n) or Sample (n−1) mode at the top.
  2. Paste your numbers separated by commas, spaces, or new lines.
  3. Read variance and standard deviation in the results panel.
  4. Review mean, count, and sum of squares for your full calculation.

Variance Formula

SS = Σ(xᵢ − mean)²
σ² = SS / n  |  s² = SS / (n − 1)
SD = √variance
  • SS = sum of squared deviations
  • σ² = population variance (divide by n)
  • s² = sample variance (divide by n − 1)

Worked Example

For 12, 15, 18, 20, 22, 25: Mean = 18. SS = (12−18)² + (15−18)² + (18−18)² + (20−18)² + (22−18)² + (25−18)² = 36 + 9 + 0 + 4 + 16 + 49 = 114. Sample variance = 114 / 5 = 22.8. SD = √22.8 ≈ 4.77.

Frequently Asked Questions (FAQs)

What is the difference between population and sample variance?

Population divides by n; sample divides by n − 1 (Bessel's correction) when estimating a larger population.

How do you calculate variance?

Compute the mean, square each deviation from the mean, sum them (SS), then divide by n or n−1. SD = √variance.

What is sum of squares in statistics?

SS = Σ(xᵢ − mean)² — total squared distance from the mean. Variance is SS divided by n or n−1.

What is standard deviation?

Standard deviation is the square root of variance. It measures spread in the same units as your original data.

When should I use sample variance instead of population?

Use sample variance when your data is a subset meant to represent a larger group — such as a survey sample or lab trial.

Why does sample variance divide by n − 1?

Bessel's correction gives an unbiased estimate of population variance from a sample. Without it, sample variance tends to underestimate true spread.

Can variance be negative?

No. Variance is always zero or positive because it is based on squared deviations. Zero variance means every value is identical.

How many numbers do I need for sample variance?

At least 2 numbers. With only one value, there is no spread to measure and n − 1 would equal zero.