Understand the statistic
What the sum of squares calculator tells you
Measuring how observations vary. Spread describes how tightly or widely values lie around a reference. It complements a center: two datasets can share the same mean while behaving very differently.
1Locate the reference center2Measure each observation’s distance3Combine distances using the displayed rule
Calculation rule
SS = Σ(xᵢ−x̄)² = Σxᵢ²−(Σxᵢ)²/n.
The formula is applied only to the observations and options you enter. No population, distribution, or sampling process is inferred automatically.
How to read the answer
Sum of squares is an unscaled measure of variation; dividing by n or n−1 produces population or sample variance.
Important: Large, nearly equal values can lose floating-point precision; consequential high-precision work may require decimal or specialist software.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the sum of squares calculator works
SS = Σ(xᵢ−x̄)² = Σxᵢ²−(Σxᵢ)²/n.
Sum of squares is an unscaled measure of variation; dividing by n or n−1 produces population or sample variance.
Worked example
Sum of Squares example
For 1, 2, 3, deviations from mean 2 are −1, 0, 1 and the corrected sum of squares is 2.
SS = Σ(xᵢ−x̄)² = Σxᵢ²−(Σxᵢ)²/n.
Supported inputs
Precision and limits
Model and design
Large, nearly equal values can lose floating-point precision; consequential high-precision work may require decimal or specialist software.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Sum of squares is an unscaled measure of variation; dividing by n or n−1 produces population or sample variance.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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