Sample and population standard deviation and variance, both shown, with the working.
Separate them with commas, spaces or new lines.
Textbook set
Population σ is exactly 2
2, 4, 4, 4, 5, 5, 7, 9Measurements
A sample from a larger batch
10.2
10.4
9.8
10.1
10.5No spread at all
Identical values
7, 7, 7, 7Textbook set
Population σ is exactly 2
2, 4, 4, 4, 5, 5, 7, 9Measurements
A sample from a larger batch
10.2
10.4
9.8
10.1
10.5No spread at all
Identical values
7, 7, 7, 7Commas, spaces or one per line.
Both are shown. Pick the one that matches what your numbers are.
The mean, sum of squares and divisor are listed so you can verify the result by hand.
Sample and population figures are shown together. Tools that quietly pick one are the reason so many reported standard deviations are wrong by a factor of √(n/(n−1)).
Mean, sum of squared deviations and the divisor are all shown. That is enough to reproduce the result on paper, which is what makes it checkable.
Uses a one-pass algorithm that tracks the running mean, rather than the E[x²] − E[x]² shortcut which can return a negative variance on large values with a small spread.
Paste a list of numbers and get the standard deviation and variance for both a sample and a population, side by side, so you are never guessing which one the tool picked. The intermediate steps are shown too — the mean, the sum of squared deviations, and the divisor used — because the sample-versus-population choice is the part people get wrong and seeing n against n−1 is what makes it clear. Variance is computed with a numerically stable one-pass algorithm rather than the textbook shortcut, which loses precision badly on large values with a small spread.
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