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--- c:ms:2017:schedule:week03 [2017/04/05 08:06] – hkimscil
+++ c:ms:2017:schedule:week03 [2022/05/15 11:25] (current) – [Central Tendency] hkimscil
@@ Line 1: / Line 1: @@
-====== Week 3 내용 ======
+ㄹ====== Week 3 내용 ======
 ===== SPSS =====
 <del>Chapter 3</del>, Chapter 4
@@ Line 107: / Line 107: @@
   * [[:Standard Deviation]] 표준편차
-  * Variance calculation formula
+  * Variance calculation formula <wrap #variance_calculation_formula />
-    * {{anchor:variance_calculation_formula}} $\displaystyle S_x^2 = \displaystyle \frac {\Sigma X^2 - \frac{(\Sigma X)^2}{N} } {N-1} $
+    * $ \displaystyle S_x^2 = \displaystyle \frac {\Sigma X^2 - \frac{(\Sigma X)^2}{N} } {N-1} $
-    * $\displaystyle \sigma_x^2 = \displaystyle \frac {\Sigma X^2 - \frac{(\Sigma X)^2}{N} } {N} = \displaystyle \frac {\Sigma X^2}{N} - \frac {(\Sigma X)^2}{N^2} = \displaystyle \frac {\Sigma X^2}{N} - \bigg(\frac {\Sigma X}{N}\bigg)^2 = \displaystyle \frac {\Sigma X^2}{N} - \mu^2   $
+    * $ \displaystyle \sigma_x^2 = \displaystyle \frac {\Sigma X^2 - \frac{(\Sigma X)^2}{N} } {N} = \displaystyle \frac {\Sigma X^2}{N} - \frac {(\Sigma X)^2}{N^2} = \displaystyle \frac {\Sigma X^2}{N} - \bigg(\frac {\Sigma X}{N}\bigg)^2 = \displaystyle \frac {\Sigma X^2}{N} - \mu^2 $
   * [[:Degrees of Freedom]] N-1
@@ Line 135: / Line 135: @@
 와 같다.
-이렇게 얻은 샘플들(k 개의)의 평균인 $A_k$ 는,
+이렇게 얻은 샘플들(k 개의)의 평균인 $ A_k $ 는,
-$$A_k = \displaystyle \frac{(X_1 + X_2 + . . . + X_k)}{k} = \frac{S_{k}}{k} $$
+$$ A_k = \displaystyle \frac{(X_1 + X_2 + . . . + X_k)}{k} = \frac{S_{k}}{k} $$
 라고 할 수 있다.
@@ Line 143: / Line 143: @@
 이때,
 $$
 \begin{align*}
 E[S_k] & = E[X_1 + X_2 + . . . +X_k] \\
@@ Line 151: / Line 151: @@
 $$
 $$
 \begin{align*}
 Var[S_k] & = Var[X_1 + X_2 + . . . +X_k]  \\
@@ Line 161: / Line 161: @@
 이다.
-그렇다면, $A_k$ 에 관한 기대값과 분산값은:
+그렇다면, $ A_k $ 에 관한 기대값과 분산값은:
 $$
 \begin{align*}
 E[A_k] & = E[\frac{S_k}{k}] \\