Enter your data set and choose whether to calculate sample variance or population variance. The Population Variance Calculator computes the variance, standard deviation, mean, sum of squares, and count from any list of numbers you provide. Paste or type values separated by commas, spaces, or line breaks.
Variance (σ² / s²)
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Standard Deviation
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Mean (x̄)
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Sum of Squares (SS)
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Count (n)
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Population variance (σ²) measures how spread out all values in an entire population are around the mean. It is calculated by summing the squared differences between each value and the mean, then dividing by the total number of values (n). A higher variance indicates greater spread in the data.
Population variance divides the sum of squared deviations by n (the total count), while sample variance divides by n−1. The n−1 denominator in sample variance (Bessel's correction) corrects for the bias that occurs when estimating a population parameter from a subset of data. Use population variance only when you have data for every member of the group.
The population variance formula is σ² = Σ(xᵢ − μ)² / n, where μ is the population mean, xᵢ are the individual values, and n is the total count. For sample variance, the formula is s² = Σ(xᵢ − x̄)² / (n−1), using the sample mean x̄ and dividing by n−1.
First, find the mean by summing all values and dividing by n. Second, subtract the mean from each value to get the deviation. Third, square each deviation. Fourth, sum all squared deviations to get the Sum of Squares (SS). Finally, divide SS by n for population variance or by n−1 for sample variance.
Use population variance when your data set contains every individual in the group you are studying. Use sample variance when your data is a subset drawn from a larger population and you want to estimate the population's variance. In most real-world research and statistics, sample variance is the appropriate choice.
A low variance means that data points are clustered closely around the mean, indicating consistency. A high variance means that values are widely spread from the mean, indicating greater variability. Variance is particularly useful for comparing the spread of two or more data sets with the same units.
Standard deviation is simply the square root of variance. While variance is expressed in squared units (e.g. kg²), standard deviation is in the same units as the original data (e.g. kg), making it easier to interpret. Both measure dispersion, but standard deviation is more commonly reported in practical contexts.
No. Variance is always zero or positive because it is computed from squared deviations, which are never negative. A variance of zero means all values in the data set are identical. Any positive variance indicates that at least some values differ from the mean.