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Variance Calculator

Paste or type a list of numbers. We compute the mean, count, both sample and population variance, and the corresponding standard deviations — useful for stats homework, quick analysis, and sanity-checking spreadsheets.

Comma-, space-, or line-separated. Decimals and negatives are fine. Anything that isn't a number is silently ignored.

Variance & spread

Sample variance (s²)

4.5714

divided by n − 1 (n = 8)

Mean (μ)5
Count (n)8
Sum (Σx)40
Sample variance4.5714
Population variance4
Sample std dev (s)2.1381
Population std dev (σ)2

Examples

Wikipedia textbook set: 2, 4, 4, 4, 5, 5, 7, 9

sample var ≈ 4.571 · pop var = 4.000

10, 12, 23, 23, 16, 23, 21, 16

mean 18.0 · sample var ≈ 24.0

−5, 0, 5, 10

mean 2.5 · sample var ≈ 41.67

How it works

We compute the mean, then sum the squared distance of each value from the mean. Dividing by n gives population variance; dividing by n − 1 gives sample variance.

Mean · μ = (Σx) ÷ n

Sample variance · s² = Σ(x − μ)² ÷ (n − 1)

Population variance · σ² = Σ(x − μ)² ÷ n

Frequently asked questions

Sample variance divides by n − 1 (Bessel's correction) — it's the right choice when your data is a sample from a larger population. Population variance divides by n and is correct only when you have data for the entire population. Most real-world stats use the sample formula.

Comma-separated, space-separated, or one per line — all work. The calculator strips empty entries and ignores anything that isn't a valid number. Negative numbers and decimals are fine.

Standard deviation is the square root of variance. The variance is in the squared units of your data; the standard deviation is in the original units, which is why it's usually easier to interpret.

When every value in your dataset is the same, there's no spread — both variance and standard deviation are exactly zero. With a single value, sample variance is undefined (you'd divide by zero); population variance is zero.