Variance Calculator

Calculate population and sample variance with step-by-step solutions — built for FBISE, CBSE, IGCSE, O Levels, A Levels & IB students.

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What is Variance?

Variance measures how spread out a dataset is from its mean. It is the average of the squared differences from the mean — always non-negative.

Formulas

Population

σ² = Σ(xᵢ − μ)² / N

Sample

s² = Σ(xᵢ − x̄)² / (n − 1)

Curriculum Notes

FBISE / CBSE — both σ² and s² appear in Class 11–12 Statistics.
O Levels / IGCSE — population variance is the standard formula tested.
A Levels / IB — both types tested; context determines which to use.

Related Tools

σ Standard Deviation x̄ Mean / Median / Mode Z Z-Score Calculator Q Quartile & IQR
Learn More

Understanding Variance

Population vs Sample Variance

Use population variance when you have data for every member of the group — for example, all students in a class. Use sample variance when your data is a subset drawn from a larger population, such as 30 students sampled from a school of 1,000.

Sample variance divides by (n − 1) rather than n. This is called Bessel's correction, and it compensates for the tendency of a sample to underestimate the true spread of the full population.

Variance and Standard Deviation

Variance and standard deviation both measure spread, but variance expresses it in squared units, which can be hard to interpret directly. Standard deviation is simply the square root of variance, bringing the measure back into the original units of the data.

For example, if your data is in metres, variance is in metres² while standard deviation is in metres — which makes it far easier to compare against the original values.