Sum of Squares Calculator
Calculate the total sum of squared deviations from the mean, a building block for variance and regression.
Sum of Squares (SS)
20.0000
Sum of Squares (SS) vs Value 1
公式
## 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)
计算示例
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
常见问题
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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