Enter your data set as comma-separated numbers, choose Sample or Population, and the Variance Calculator returns the variance, standard deviation, mean, count (n), and sum of squares — all computed from your values in one step.
Variance
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Standard Deviation
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Mean
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Count (n)
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Sum of Squares (SS)
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Variance is a statistical measure of how spread out data points are from their mean. A low variance means data points are clustered close to the mean, while a high variance means they are widely dispersed. It is calculated as the average of the squared differences from the mean.
Population variance (σ²) divides the sum of squared differences by n (the total count), and is used when you have data for an entire population. Sample variance (s²) divides by n−1 instead, applying Bessel's correction to produce an unbiased estimate when your data is a subset of a larger population.
Use population variance only if your data set represents the complete population you are studying. In most real-world research and analysis, you are working with a sample, so sample variance (dividing by n−1) is the appropriate choice. When in doubt, use sample variance.
First, find the mean by summing all values and dividing by n. Then subtract the mean from each data point and square each result. Sum all those squared differences to get the Sum of Squares (SS). Finally, divide SS by n for population variance or by n−1 for sample variance.
Standard deviation is simply the square root of variance. While variance expresses spread in squared units (which can be hard to interpret), standard deviation is expressed in the same units as your original data, making it more intuitive for practical interpretation.
Type or paste your numbers into the Data Set field, separated by commas, spaces, or line breaks. You can copy data directly from a spreadsheet or document. Non-numeric values and empty entries are automatically ignored.
The Sum of Squares is the total of all squared deviations from the mean: SS = Σ(xᵢ − x̄)². It is an intermediate step in computing variance — variance equals SS divided by n (population) or n−1 (sample). A larger SS indicates greater overall spread in the data.
No. Variance is always zero or positive because it is based on squared differences, and squaring any real number always produces a non-negative result. A variance of zero means all data points are identical.