What does variance measure?

Variance is the average of the squared distances from the mean. Big variance means the values are spread far from the centre; near-zero variance means they cluster tightly.

Sample or population — which do I pick?

If your numbers are everything you care about (a whole class, a full season), use population. If they are a draw from something bigger (survey responses, test batches), use sample — dividing by n − 1 corrects the underestimate.

Why square the deviations?

Raw deviations always sum to zero — the positives and negatives cancel. Squaring makes everything positive and, as a bonus, punishes big deviations more than small ones.

How is variance related to standard deviation?

Standard deviation is the square root of variance — the same spread converted back into the original units, which is why it is usually the number people quote.

Stats & Algebra

Variance Calculator

How spread out is your data? Get the variance and standard deviation with the full deviation table worked out row by row.

Your numbers

Data type

Your numbers

5 numbers recognised

Separate with commas or spaces — up to 60 values.

Worked solution

Sample variance s²

standard deviation ≈ 3.1623 — the spread in the original units

The values sit, on average, about 3.1623 away from the mean of 10. Variance is that spread measured in squared units.

The working

3 steps

Find the mean
mean = 50 ÷ 5 = 10
Measure each value's distance from the mean
Deviations can be negative, which is why the next step squares them — otherwise they would cancel out.
x x − mean (x − mean)²
6 -4 16
8 -2 4
10 0 0
12 2 4
14 4 16
Sum of squared deviations = 40
Divide by n − 1 (sample)
Sample data divides by n − 1 — Bessel's correction — because a sample tends to underestimate the true spread.
s² = 40 ÷ 4 = 10
Variance (s²)
10
Standard deviation (s)
3.1623

x	x − mean	(x − mean)²
6	-4	16
8	-2	4
10	0	0
12	2	4
14	4	16

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Studying statistics or linear algebra? See every tool in the Stats & Algebra hub — variance, interpolation, RREF and eigenvectors, cross-linked.

Why n − 1 for samples?

A sample's mean is computed from the same values you are measuring spread around, so it sits a little too close to them — the squared deviations come out slightly small on average. Dividing by n − 1 instead of n (Bessel's correction) cancels that optimism. For large samples the difference barely matters; for small ones it is essential.