Sum of Squares Calculator
Calculate the sum of squared deviations from the mean.
Sum of Squares Formula
For observations xᵢ with mean x̄, the total sum of squares is SS = Σ(xᵢ − x̄)². It measures how much the values vary around their average.
Why It Matters
Sum of squares is used in variance, standard deviation, regression and ANOVA calculations.
Understanding Sum of Squares
Sum of squares measures total squared deviation and is a building block for variance, regression and ANOVA calculations.
Sum of Squares Example
For values 2, 4 and 6 with mean 4, squared deviations are 4, 0 and 4, producing a sum of squares of 8.
Why It Matters
Because deviations are squared, larger departures from the mean receive more weight. Different forms of sum of squares are used for total, between-group and residual variation.
Frequently Asked Questions
Can sum of squares be negative?
No.
Is it the same as variance?
No. Variance divides a sum of squares by an appropriate degrees-of-freedom term.
Where is it used?
Commonly in ANOVA, regression and variance calculations.
Methodology, Assumptions and Interpretation
Sum of squares measures squared deviations, but the reference matters: total SS uses deviations from the overall mean, while regression and residual SS partition variability differently. Always match the formula to the statistical model being used.