Enter your data set as a list of numbers (separated by commas, spaces, or line breaks) and choose between sample or population variance. The Variance Calculator returns the variance, standard deviation, mean, count (n), and sum of squares — giving you a complete statistical summary of your data.
Variance
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Standard Deviation
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Mean (Average)
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Count (n)
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Sum of Squares (SS)
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Sum of Values
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Variance is a statistical measure of how spread out data points are relative to their mean. A low variance means data points cluster closely around the mean, while a high variance means they are spread further apart. 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 (Bessel's correction) and is used when your data represents a subset of a larger population. Using n−1 for samples produces an unbiased estimate of the true population variance.
Use population variance only if your data set contains every member of the group you're studying. In most real-world situations — surveys, experiments, research studies — you're working with a sample, so sample variance is the appropriate choice. When in doubt, use sample variance.
First, find the mean of your data set by summing all values and dividing by n. Next, subtract the mean from each value to get the deviation, then square each deviation. Sum all the squared deviations 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 is expressed in squared units (which can be harder to interpret), standard deviation is in the same units as your original data, making it more intuitive. Both measure the spread of data, but standard deviation is generally easier to communicate.
Yes, variance can be calculated for any data set with at least two values (for sample variance) or one value (for population variance). However, very small data sets may not produce statistically reliable results, so results should be interpreted with caution.
A variance of zero means all values in your data set are identical — there is no spread at all. Every data point equals the mean, so there are no deviations and the sum of squares is zero.
The Sum of Squares (SS) is the total of all squared differences between each data point and the mean: SS = Σ(xᵢ − x̄)². It is an intermediate step in computing variance. Variance is simply SS divided by n (population) or n−1 (sample).