Math & Statistics
Variance Calculator
Calculate the population mean, population variance, population standard deviation, and range for exactly five entered values. The page uses a population denominator of five and distinguishes that convention from sample variance.
Mean-
Population variance-
Population standard deviation-
Range-
Decision view
Observations around the arithmetic mean
Observations around the arithmetic meanEach point is positioned on the entered-value scale and connected to the mean so the signed deviations behind variance are visible.
Exact scenario comparisonValue 5 changes while all other entered assumptions remain constant.
| Value 5 | Mean | Population variance | Population standard deviation | Range |
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How to use Variance Calculator
- Enter five observations expressed in the same unit and verify that the five values are intended to represent the complete population for this calculation.
- Read the mean as the center, population variance as average squared deviation, and population standard deviation as spread on the original unit scale.
- If the five observations are a sample from a wider population, use an analysis that divides the squared-deviation total by n minus one and documents the sampling design.
Calculator guide
Understanding Variance Calculator
Variance measures spread by converting every deviation from the mean into a squared distance and averaging those squared distances. Because the units are squared, the accompanying standard deviation is often easier to interpret on the original measurement scale.
Calculation method
How the calculation works
Calculate the five-value mean, average squared deviation from that mean, and the corresponding population standard deviation. Calculate the five-value mean, average squared deviation from that mean, and the corresponding population standard deviation.
Calculation audit
Trace variance from observations to spread
A variance result is easiest to verify as a short ledger rather than as a single formula.
Keep full precision through the intermediate steps and round only the reported values.
Worked situations
Practical examples
- For 10, 12, 15, 18, and 20, the mean is 15; squared deviations are 25, 9, 0, 9, and 25.
- Those squared deviations total 68, so the displayed population variance is 68 divided by 5, or 13.6.
- The population standard deviation is the square root of 13.6, approximately 3.688, which returns the spread to the original unit.
Better inputs
Useful tips
- Choose the population or sample convention before calculating; changing the denominator after reporting creates inconsistent results.
- Investigate data-entry errors and measurement limits because squaring gives large deviations disproportionate influence.
- Pair standard deviation with the mean, count, and distribution shape; datasets with different structures can share the same variance.
Before relying on the result
Limitations and common mistakes
- The calculator is fixed to five values and uses population variance, dividing by five rather than four.
- Variance and standard deviation do not identify skew, multimodality, time order, or the source of unusual observations.
- The result is descriptive only and does not provide confidence intervals, hypothesis tests, weights, missing-data handling, or robust spread measures.
Reference
Key terms
- Deviation
- An observation minus the arithmetic mean.
- Population variance
- The sum of squared deviations divided by the population count.
- Population standard deviation
- The square root of population variance, expressed in the original unit.
- Sample variance
- An estimator that commonly divides the squared-deviation sum by n minus one.
Important note
Calculated directly from the entered values using the displayed formula and rounding settings.
Frequently asked questions
Why does this variance differ from spreadsheet VAR.S?
VAR.S uses the sample denominator n minus one. This calculator uses population variance, equivalent to a population-variance function such as VAR.P.
Can variance be negative?
No. Squared deviations are nonnegative, so a correctly calculated variance cannot be below zero.
Why is variance zero?
Variance is zero only when all five entered values are identical.
Should variance be reported instead of standard deviation?
Variance is central to statistical methods, while standard deviation is usually easier to explain because it uses the original measurement unit.