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Variance Calculator

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

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.

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