Enter a list of numbers to calculate variance.
Show both denominators, standard deviation and every squared deviation from the mean.
| x | x − mean | (x − mean)² |
|---|
Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.
Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.
Use the interactive product above first. These notes add interpretation, verification and limits below the results and product controls.
Population variance divides by N because the listed values are the full population. Sample variance divides by N−1 to estimate population spread from a sample. Record which definition the downstream report expects before copying a result.
Variance squares each distance from the mean, so a single extreme observation can dominate the result. Use the deviation evidence above to identify which values contribute most before interpreting a large variance as broad spread.
If the data are measured in centimeters, variance is in square centimeters. Standard deviation returns to the original unit and is often easier to interpret, while variance is especially useful inside statistical formulas and model comparisons.
Prematurely rounding the mean or individual deviations can noticeably change variance in small datasets. Keep full internal precision, then round the displayed result to a level supported by the source measurements.
Variance is mathematically useful but its squared units can make practical interpretation awkward. Taking the square root gives standard deviation in the original measurement unit; comparing both values helps separate a calculation check from a user-facing description of typical spread.
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