Variance Calculator

Variance measures how far a set of numbers spreads out around their mean. You subtract the mean from each value, square the result so positive and negative differences do not cancel, and average those squared differences. A small variance means values cluster tightly near the mean; a large variance means they are scattered widely.

Population variance divides the sum of squared deviations by n and is correct when your data covers every value in the group. Sample variance divides by n minus 1 (Bessel's correction) and is the right choice when your data is a subset drawn from a larger group, which fits most real surveys and experiments.

Find the mean. Subtract the mean from each value to get deviations. Square each deviation. Sum the squared deviations. Divide by n for population variance or by n minus 1 for sample variance. The calculator shows the deviations and squared deviations for the first 10 values so you can verify each step.

The coefficient of variation expresses standard deviation as a percentage of the mean: CV = SD / |mean| x 100. It lets you compare the relative spread of datasets with very different units or scales. CV is undefined when the mean is zero.

Standard deviation is the square root of variance. Variance lives in squared units (dollars squared, kilograms squared) which is awkward to read, while standard deviation returns to the original units of your data. Both describe the same spread.