Variance

Variance is the average of the squared differences between each value and the mean, measuring how spread out a dataset is around its center.

Where the range looks only at the two extremes, variance uses every value. It asks how far each point sits from the average, squares those distances (so positives and negatives do not cancel, and larger gaps count more heavily), and averages the result. A small variance means values huddle near the mean; a large variance means they scatter widely.

How variance relates to a chart

Variance is not drawn directly, but it explains a chart's shape. A dataset with low variance produces a tall, narrow histogram clustered around the mean; high variance produces a short, wide one spread across the axis. Because variance is in squared units (squared dollars, squared centimetres), people usually report its square root — the standard deviation — which is back in the original units and easier to interpret on a chart.

A worked example

Take the values 2, 4, 4, 6. Their mean is (2 + 4 + 4 + 6) ÷ 4 = 4. The deviations from the mean are −2, 0, 0, +2. Squaring gives 4, 0, 0, 4, which sum to 8. Dividing by the four values gives a variance of 8 ÷ 4 = 2. The standard deviation is the square root of 2, about 1.41 — telling you the typical value sits roughly 1.4 units from the mean of 4.

Related terms

Variance is the square of the standard deviation, and it complements the median as a way to summarise data. It is a richer measure of spread than the range. To compute it on your own numbers, use the standard deviation calculator.