Sample variance, standard deviation and mean — with worked steps
Enter your data to calculate the variance instantly. The calculator also shows the mean, standard deviation and a full step-by-step breakdown.
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Variance measures how far a set of numbers is spread out from their mean. It is the average of the squared deviations from the mean. Squaring the deviations keeps positive and negative differences from cancelling out and gives extra weight to values that lie far from the centre.
Variance and standard deviation describe the same spread, just on different scales: the standard deviation is simply the square root of the variance. Variance is expressed in squared units (for example, "dollars squared"), which is why the standard deviation — back in the original units — is often easier to interpret. This page reports both.
Sample variance divides the sum of squared deviations by n − 1 and estimates the variance of a larger population from a sample. Population variance divides by n and is used when your numbers represent the whole group. The calculator above reports the sample variance; the population variance is the square of the population standard deviation shown in the additional statistics.
Standard deviation is the square root of variance. Variance is in squared units; standard deviation is in the original units, which usually makes it easier to interpret.
Dividing by n − 1 (Bessel’s correction) compensates for the fact that a sample tends to underestimate the true spread of the population it came from.
No. It is an average of squared values, so it is always zero or positive, and it is zero only when every value is the same.