Calculate population and sample variance, standard deviation, and sum of squares from your dataset.
Last updated: March 2026
Min 2 values. Separate by commas or spaces.
Mean
5.0000
Sample Size (n)
8
Sum of Squares (SS)
32.0000
Variance measures how spread out data is from its mean. It's the average of the squared deviations from the mean. A small variance means data points cluster near the mean; large variance means they're scattered far from it.
There are two types: Population variance (σ²) describes all members of a complete population, dividing by n. Sample variance (s²) estimates the population variance from a sample, dividing by (n−1) to reduce bias. The (n−1) correction is called Bessel's correction.
Standard deviation (σ or s) is the square root of variance. It has the same units as the original data, making it more interpretable than variance. Most analyses use standard deviation, but variance appears in statistical formulas.
Use population variance (σ²) when analyzing the entire dataset or complete population. Use sample variance (s²) when your data is a sample from a larger population. The (n−1) denominator corrects for sample bias (Bessel's correction).
Data: 2, 4, 4, 4, 5, 5, 7, 9
Sample variance divides by (n−1) to correct for bias. Using n underestimates the true population variance. Bessel's correction makes the sample variance an unbiased estimator of the population parameter.
Squaring makes all deviations positive (so they don't cancel out) and penalizes large deviations more. It turns the problem into calculus-friendly form and makes variance the mathematical foundation of many statistical tests.
High variance indicates data is spread out far from the mean. Low variance means data clusters tightly around the mean. High variance suggests high variability or uncertainty in the dataset.
Yes, variance is zero only if all data values are identical (no variability). In practice, this rarely happens. Even slight differences in values produce non-zero variance.
Standard deviation has the same units as the original data, making it more interpretable. Variance is in 'squared units' which is harder to understand. Both measure spread; SD is more practical for communication.
Yes, variance is a general measure of spread. Unlike some tests that assume normality, variance calculation works for any distribution. However, for highly skewed data, median and IQR may be more informative than mean and variance.