Variance Calculator

Variance measures how spread out a dataset is — the average of the squared distances from the mean. It squares the deviations so positive and negative differences do not cancel out. The square root of variance is the standard deviation, which is in the original units and easier to interpret.

Population variance divides by n and is used when your data covers every member of the group. Sample variance divides by n−1 and is used when the data is a random sample estimating a larger population — the n−1 correction makes the estimate unbiased. For the dataset 2, 4, 4, 4, 5, 5, 7, 9, the population variance is 4 but the sample variance is 4.571.

Squaring serves two purposes: it makes all terms positive so they cannot cancel, and it penalizes large deviations disproportionately. A value three units away contributes nine times as much as a value one unit away. The downside is that units get squared (₹², kg²), which is why the standard deviation — the square root — is reported for everyday use.

Paste comma-separated values like student marks, share prices or monthly electricity bills. If you have every observation — all students in one class, say — choose population. If you are estimating from a sample, like a price survey, choose sample. The output gives variance, standard deviation and mean together.

It depends entirely on the scale of the data — a variance of 4 is small for income in lakhs but large for temperatures in degrees. That is why relative measures like the coefficient of variation calculator are better for comparing spread across different datasets, while variance and standard deviation describe spread in absolute terms.