Calcolatore Somma dei Quadrati
Calcola la somma dei quadrati delle deviazioni dalla media di un set di dati.
Sum of Squares (SS)
20.0000
Sum of Squares (SS) vs Value 1
Formula
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.
Esempio Risolto
Find the sum of squares for 3, 5, 7, 9.
- 01Mean = (3 + 5 + 7 + 9) / 4 = 24 / 4 = 6
- 02Deviations: 3-6=-3, 5-6=-1, 7-6=1, 9-6=3
- 03Squared deviations: 9, 1, 1, 9
- 04SS = 9 + 1 + 1 + 9 = 20
Domande Frequenti
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.
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