What is variance?
Variance measures how far a set of numbers is spread out from its mean. A low variance means the values cluster tightly around the average, while a high variance indicates they are scattered widely. In statistics the concept is fundamental: it underpins hypothesis testing, confidence intervals, regression analysis, and quality control. The square root of the variance gives the standard deviation, which is expressed in the same units as the original data and is often easier to interpret.
Population vs sample variance
When you have data for every member of a group—say, the test scores of every student in a class—you use population variance and divide by N. When you have only a subset of the group, you use sample variance and divide by N−1 (Bessel's correction) to produce an unbiased estimate. This calculator lets you toggle between the two with a single click so you always apply the correct formula.
How to use this calculator
Enter your numbers separated by commas or spaces—decimals and negatives are both accepted. Choose "Population" or "Sample" with the toggle, then click Calculate variance. The result card displays the variance, standard deviation, mean, count, sum, min, max, range, and the formula that was applied. Everything runs in your browser; there is no sign-up and no data is sent to a server.
Practical applications
Finance professionals use variance to measure portfolio risk—higher variance signals more volatile returns. Engineers use it in quality control to check whether manufactured parts stay within tolerance. Researchers analyse variance (ANOVA) to determine whether different treatments produce significantly different outcomes. Teachers compare variance in test scores to understand how uniformly students performed. In each case, variance distils an entire data set into a single number that captures spread.
Tips
Always check whether your data represents a full population or a sample before choosing a formula. If the variance seems unusually large, look for outliers—a single extreme value can inflate it dramatically. Compare the standard deviation with the mean: a standard deviation that is a large fraction of the mean indicates high relative variability. This free calculator gives you instant, accurate results on any device—bookmark it for quick access.