平方和计算器
计算一组数据相对于均值的偏差平方和。
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.
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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