Sample stdev
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Standard Deviation & Variance Calculator
Mean, sample variance, and sample standard deviation from a comma or space list of numbers.
Page updated 2026-09-14.
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Sample variance
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Mean
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How spread out a data set actually is
The numbers 12, 15, 18, 16, 21, 14 (6 values) have a mean of 16.0, a sample variance of 10.0, and a sample standard deviation of 3.1623 (the square root of variance).
Standard deviation is simply the square root of variance -- variance itself is calculated in squared units (which is why it's less intuitive to interpret directly), while standard deviation converts back to the same units as the original data, making it the more commonly reported and interpretable figure of the two.
A standard deviation of 3.16 around a mean of 16 tells you that most values in a typical dataset like this cluster within roughly one standard deviation of the mean (about 12.8 to 19.2 here) -- a quick, useful sense of how tightly or loosely the data is grouped around its center.
Why 'sample' variance divides differently than you might expect
Sample (n-1) variance. Need at least two numbers. This calculates sample variance, which divides the sum of squared deviations by (n-1) rather than n -- a correction (called Bessel's correction) that produces a less biased estimate of the true population variance when you're working with a sample rather than complete population data, which is the far more common real-world scenario.
Population variance (dividing by n instead of n-1) would be the appropriate calculation only if these 6 numbers represented the entire population of interest, not a sample drawn from a larger group -- using the wrong version for your actual situation produces a systematically biased result.
At least two numbers are required for this calculation to be meaningful at all -- with only one data point, there's no variation to measure, and dividing by (n-1) would mean dividing by zero, which is mathematically undefined.
Related statistical tools
Once you have a mean and standard deviation, the Z-Score / Normal Distribution Calculator uses both to find how unusual a specific value is relative to this distribution.
For determining how large a sample you'd need to achieve a specific confidence level in a survey or poll, the Margin of Error & Sample Size Calculator is a related statistical planning tool.
Frequently Asked Questions (FAQ)
How is the standard deviation of 3.1623 derived from the variance of 10.0?
Standard deviation is the square root of variance: sqrt(10) = 3.1623 (rounded). Variance is calculated in squared units, while standard deviation converts back to the original data's units, which is why it's typically the more interpretable figure.
Why does this divide by (n-1) instead of n?
Sample (n-1) variance. Need at least two numbers. This is sample variance, which uses (n-1) in the denominator (Bessel's correction) to produce a less biased estimate of the true population variance when the data represents a sample rather than the complete population -- the far more common situation in practice.
When would I use population variance (dividing by n) instead?
Only when your data genuinely represents the entire population of interest, not a sample drawn from a larger group. If these 6 numbers were literally every value that exists (not a subset), population variance (dividing by n) would be the technically correct calculation instead.
Why does this require at least two numbers?
Sample (n-1) variance. Need at least two numbers. With only one data point there's no variation to measure, and the (n-1) denominator would become zero with a single value, which is mathematically undefined for division.
What does a standard deviation of 3.16 actually tell me about this data?
It indicates most values cluster within roughly plus or minus 3.16 of the mean (16.0), so a typical range of about 12.8 to 19.2 covers a large share of the dataset -- a quick sense of how spread out or tightly clustered the data is around its center.
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