Sum of Squares Calculator

Enter the dataset numbers and click 'Calculate' to determine the sum of squares.

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Sum of Squares Calculator

Use this sum of squares calculator to compute both statistical and algebraic sums of squares for any dataset. It also provides step-by-step calculations for easier understanding.

What Is Sum of Squares?

Statistics:

Sum of squares (SS) measures the variability of a dataset by summing the squared deviations of each data point from the mean. A higher SS indicates greater spread within the dataset.

Algebra:

In algebra, sum of squares refers to the addition of squared terms, without necessarily involving deviations from the mean.

Sum of Squares Formulas

Statistical Calculation:

Formula:

(Xi - X̄)²

Xi = Individual data point
X̄ = Mean of the dataset

You can use our Sum of Squares Calculator for automatic computation.

Algebraic Calculation:

Formula:

n₁² + n₂² + n₃² + ... + nₙ²

n = Total numbers in the expression

Relationship Between Sum of Squares and Sample Variance

The sum of squares is closely related to sample variance:

SS: Total squared deviations from the mean.
Sample Variance (s²): Average squared deviation from the mean: s² = SS / (n - 1)

n = Sample size

Limitations of Sum of Squares

Sensitivity to Outliers: Extreme values can exaggerate spread.
Assumption of Normality: Works best with normally distributed data.
Limited Information: Indicates total variation but not direction, shape, or symmetry of distribution.