Variance calculator

Calculate population variance or corrected sample variance. Compare the mean and standard deviation alongside the result.

Result

Enter your data and run the tool. Your result will appear here.

From mean to variance

Compare the sample and population divisors.

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How to use the tool

Fill in these fields: Numbers (whitespace, ; or newlines), Dataset type.
Select “Calculate” to obtain the result.
Enter up to 10,000 values and choose population or sample.
Negative numbers and decimal points or commas are supported.
Compare the sample and population divisors.
The line marks the mean. Each dot represents an observation and the segment shows its deviation. For long series the chart shows up to 12 observations, while the calculation uses them all.

Method and principles

Formula

σ^{2} = \frac{Σ {(x_{i} - μ)}^{2}}{n}

Variance divides the sum of squared deviations from the mean by n for a population or n−1 for a sample.

Sample (divide by n−1)

s^{2} = \frac{Σ {(x_{i} - x̄)}^{2}}{n - 1}

Worked example

For 1; 2; 3, the mean is 2 and squared deviations sum to 2. Population variance is 2/3; sample variance is 1.

Variance uses squared units. If the variance is 4 m², the standard deviation is 2 m, in the original unit.

Practical example

Input

Numbers (whitespace, ; or newlines): 1; 2; 3
Dataset type: Population (divide by n)

Result

σ^{2} = \frac{1 + 0 + 1}{3} = \frac{2}{3}

Limits and interpretation

Variance is measured in squared units. A single observation has population variance 0; sample variance requires at least two observations.

Result details

Result details
Parameter	Value
Observations	3
Arithmetic mean	2
Variance	0.666666666667
Standard deviation	0.816496580928
Divisor	3

Limits and checks

Limits and checks
Parameter	Value
Numbers (whitespace, ; or newlines)	≤ 200000 characters

Variance calculator

Set your data

Result

From mean to variance

How to use the tool

Method and principles

Formula

Sample (divide by n−1)

Worked example

Practical example

Limits and interpretation

Result details

Limits and checks

Favorites

Variance calculator

Set your data

Result

How to use the tool

Method and principles

Formula

Sample (divide by n−1)

Worked example

Practical example

Limits and interpretation

Result details

Limits and checks

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