Toggle between sample and population variance for any data set, with standard deviation and mean alongside it.
Computed in your browser from the data above.
Variance measures how far each value in a data set sits from the mean, squared and averaged. A low variance means values cluster tightly; a high one means they scatter widely. For the default set (4, 8, 6, 5, 3, 7): mean = 5.5; sum of squared deviations = 17.5; sample variance = 17.5 / 5 = 3.5; standard deviation = square root of 3.5 = 1.871.
Variance is one of several ways to describe how spread out a data set is, and each one trades simplicity for sensitivity differently:
Range is the fastest gut check, IQR is the one least thrown off by a single bad data point, and variance uses every value but weights outliers hardest. See the standard deviation calculator for sample and population figures side by side, or the percentile calculator to pull the IQR's two endpoints directly.
This tool is built as a single toggle rather than dual output, so switching the Type field recomputes the one variance you asked for. If you'd rather see sample and population figures side by side without switching, the standard deviation calculator on this site reports both at the same time.
No. Every deviation from the mean gets squared before it's averaged, and a squared number can't be negative. The smallest possible variance is zero, which happens only when every value in the data set is identical.
Because the formula squares each deviation before averaging it. If your data is in dollars, variance comes out in dollars squared, which is awkward to interpret directly. Standard deviation, variance's square root, returns to the original units and is usually the more readable figure for describing spread.
Zero, for both Sample and Population. A single value has no deviation from its own mean, so the sum of squared deviations is zero regardless of which divisor the Type toggle selects.