Variance Calculator

How to use the variance calculator

1. Fill in the fields — they start with a worked example.
2. Read the answer, and the arithmetic shown beneath it.
3. Copy the results, or adjust the inputs to compare scenarios.

About this tool

Variance measures how far a set of numbers sits from its own mean, and standard deviation is its square root — the same measure expressed in the units of the original data, which is why it is the one usually quoted.

The decision that changes the answer is whether the numbers are a sample or the whole population. A population variance divides the summed squared deviations by n. A sample variance divides by n − 1, because a sample's own mean sits closer to the sample than the true mean does, which makes the spread look smaller than it is; dividing by one less corrects that bias. Nearly every real dataset is a sample, so the sample figure is usually the one you want, and both are shown here rather than one being chosen silently.

The correction matters most exactly when it is easiest to overlook. With ten values the two differ by about eleven per cent, and with five values by twenty-five — small datasets being the ones people are most likely to work through by hand.

Quartiles use linear interpolation, the method spreadsheets and most statistics packages use. Quartile definitions genuinely differ between implementations, so a figure that disagrees with another tool by a small margin is usually this rather than an error. Outliers are flagged at the conventional 1.5 times the interquartile range beyond each quartile, which is a convention rather than a test — a flagged value is worth looking at, not deleting.

Common uses

• Getting standard deviation for a set of measurements or results.
• Checking whether a dataset contains outliers before averaging it.
• Seeing the difference the sample correction makes on a small dataset.

Frequently asked questions

What is the difference between sample and population variance?

Population variance divides by n; sample variance divides by n − 1. The correction exists because a sample's own mean sits closer to it than the true mean does, which understates the spread.

Which one should I use?

The sample figure, unless your numbers are genuinely the entire population — every employee rather than a survey of them. Most data is a sample.

Why do my quartiles differ from another tool?

Because quartile definitions differ between implementations. This uses linear interpolation, as spreadsheets and most statistics packages do, so small disagreements are expected rather than errors.