Standard Deviation and Variance: What They Mean and How to Read Them

Two core measures of how spread out your data is around the mean: variance and standard deviation. Learn the calculation logic and how to interpret them.

What is variance?

Each observation’s difference from the mean is squared, and those squares are summed and divided by the number of observations (or n-1 for a sample). Squaring prevents positive and negative differences from canceling each other out.

What is standard deviation?

It’s the square root of the variance. Taking the square root brings the measure back to the original unit of the data — which is why standard deviation is reported and interpreted far more often than variance.

Example: If a class’s exam scores have a standard deviation of 4 points, students’ scores typically fall within roughly ±4 points of the mean.

How to interpret it

• Small standard deviation: observations cluster close to the mean — the data is homogeneous.
• Large standard deviation: observations spread far from the mean — the data is heterogeneous or contains outliers.
• When comparing two groups on the same scale with different standard deviations, comparing means alone can be misleading.

Standard deviation and variance matter precisely where a single summary number falls short: two groups can share the same mean while having very different spreads, which can point to very different practical conclusions.