Calculateur de Somme des Carrés

Calculez la somme des carrés d'un ensemble de valeurs.

Sum of Squares (SS)

20.0000

Moyenne6.0000
Population Variance (SS/n)5.0000

Sum of Squares (SS) vs Value 1

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Formule

How to Calculate the Sum of Squares

Formula

SS = Sum of (xi - mean)^2

For each value, subtract the mean, square the result, and add them up. The sum of squares quantifies total variability in the data and is the numerator in variance calculations.

  • Population Variance = SS / n
  • Sample Variance = SS / (n - 1)

    • Exemple Résolu

    Find the sum of squares for 3, 5, 7, 9.

    1. 01Mean = (3 + 5 + 7 + 9) / 4 = 24 / 4 = 6
    2. 02Deviations: 3-6=-3, 5-6=-1, 7-6=1, 9-6=3
    3. 03Squared deviations: 9, 1, 1, 9
    4. 04SS = 9 + 1 + 1 + 9 = 20

    Questions Fréquentes

    Why square the deviations instead of just summing them?

    If you sum the raw deviations, positive and negative differences cancel out and the sum is always zero. Squaring ensures all terms are positive and gives extra weight to large deviations.

    What is the relationship between SS, variance, and standard deviation?

    Variance = SS / n (or SS / (n-1) for samples). Standard deviation = sqrt(Variance). The sum of squares is the fundamental building block.

    How is SS used in ANOVA?

    In ANOVA, total SS is partitioned into between-group SS and within-group SS to test whether group means differ significantly.

    Apprendre

    Understanding the Normal Distribution

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