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Standard Deviation and Variance Calculator — result sheet
Measure data spread using population or sample standard deviation, with variance and mean.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Population variance = sum((x - mean)^2)/n; sample variance = sum((x - mean)^2)/(n-1); SD = sqrt(variance).
Use population mode when the list is the entire group you want to describe. Use sample mode when estimating population variability from a sample; dividing by n - 1 is Bessel's correction for the variance. Standard deviation has the same units as the observations, while variance has squared units.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Values — Up to 1,000 comma- or whitespace-separated numbers, each between -1e12 and 1e12.
- Data interpretation — 2 choices
Worked example
| Input | Value |
|---|---|
| Values | 2, 4, 4, 4, 5, 5, 7, 9 |
| Data interpretation | population |
2
Assumptions and limits
- Population mode requires at least one value; sample mode requires at least two.
- Every observation has equal weight. Sample variance is unbiased under independent, identically distributed sampling, but sample standard deviation itself need not be unbiased.
- Lists contain at most 1,000 finite numbers and 32,000 characters. A centered, corrected two-pass computation limits cancellation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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