Education
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.
Sample variance (s²)
4.5714
divided by n − 1 (n = 8)
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.
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