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Variance Calculator

Calculate sample or population variance of a data set with each squared deviation shown step by step.

Also known as sample variance, population variance, variance formula.

Enter values

Separate values with commas, spaces or new lines.

Results update as you type.

Result

Sample variance s²

27.42857143

Standard deviation
5.23722937
Mean
18
Sum of squares
192
Step-by-stepShow
  1. Mean = 18
  2. Σ(x − x̄)² = 192
  3. Variance = 192 ÷ (n − 1) = 7 = 27.42857143

Deviations

xx − x̄(x − x̄)²
10-864
12-636
23525
23525
16-24
23525
2139
16-24

About the Variance Calculator

Calculate sample or population variance of a data set with each squared deviation shown step by step.

Also known as: sample variance, population variance, variance formula, σ² calculator.

How to use this calculator

  1. Enter data set, data is a.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Open “Step-by-step” to see how the answer was worked out.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Variance formula

s² = Σ(x − x̄)² / (n − 1) · σ² = Σ(x − μ)² / N

Worked example

Using the values pre-filled in the calculator above:

  • Data set: 10, 12, 23, 23, 16, 23, 21, 16
  • Data is a: Sample

the calculator returns:

  • Sample variance s²: 27.42857143
  • Standard deviation: 5.23722937
  • Mean: 18
  • Sum of squares: 192

Working

  1. Mean = 18
  2. Σ(x − x̄)² = 192
  3. Variance = 192 ÷ (n − 1) = 7 = 27.42857143