제곱합 (Sum Of Square)

$$ \begin{displaymath}\begin{split} S &= \sum (x_{i}-\overline{x})^{2} \\ &= \sum x_{i}^{2}-(\sum x_{i})^{2}/n \\ &= \sum x_{i}^{2}-CT \end{split}\end{displaymath} $$ * 단, $CT$는 [[수정항]] $\left( CT=\frac{(\sum x_{i})^{2}}{n}=n(\overline{x})^{2} \right) $

$$ S = \left\{ \sum X_{i}^{2} - (\sum X_{i})^{2}/n \right\} \times \frac{1}{h^{2}} $$

• 단, $X_{i}=(x_{i}-x_{0}) \times h$

$$ E(S) = (n-1) \cdot \sigma^{2} $$

$$ Var(S) = \left( \sqrt{2(n-1)} \cdot \sigma^{2} \right)^{2} $$