Measure how far data values spread around their mean, with the correct divisor for a sample or a full population.
For 2, 4, 4, 4, 5, 5, 7, 9, the population variance is 4. Treating those eight values as a sample gives 32/7 ≈ 4.5714.
8 values; divide the squared-deviation sum 32 by 8.
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How to Use the Variance Calculator
Paste or type your numerical observations. Choose Entire population if they include every member of the group you want to describe. Choose Sample if they are observations drawn from a larger group. The result, divisor, mean, and standard deviation update when you calculate.
Population Variance Versus Sample Variance
Both formulas sum squared distances from the mean. Population variance divides by the number of observations N. Sample variance uses n − 1 as its divisor when estimating population variation from a sample. With just one observation, sample variance is undefined.
s² = Σ(x − x̄)²/(n − 1)
Worked Example: Eight Observations
For 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5. The squared differences are 9, 1, 1, 1, 0, 0, 4, and 16, totaling 32. Population variance is 32/8 = 4. Sample variance is 32/7 ≈ 4.5714.
What Does Variance Tell You?
A larger variance means values tend to be farther from their mean. Variance is expressed in squared units: if the observations are centimeters, the variance is in square centimeters. Standard deviation is the square root of variance and returns to the original unit.
Common Variance Mistakes
Do not divide sample squared deviations by n when you need sample variance. Do not average signed deviations; they cancel to zero. Square each deviation before summing, and keep all observations, including repeated values.
Variance Calculator FAQs
What is the difference between sample and population variance?
Sample variance divides by n − 1; population variance divides by N.
Can sample variance be calculated from one value?
No. The divisor n − 1 would be zero.
What does zero variance mean?
All entered values are identical.
Method and references
The population and sample formulas follow the educational reference linked below. Check whether your assignment calls for sample or population variance before comparing answers.
Sources
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Disclaimer
For educational use. Check your class or textbook convention when the problem defines a different range, sequence index, or notation.