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c:ms:2017:schedule:week03 [2017/04/05 08:06] hkimscilc:ms:2017:schedule:week03 [2022/05/15 11:25] (current) – [Central Tendency] hkimscil
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-====== Week 3 내용 ======+====== Week 3 내용 ======
 ===== SPSS ===== ===== SPSS =====
 <del>Chapter 3</del>, Chapter 4 <del>Chapter 3</del>, Chapter 4
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   * [[:Standard Deviation]] 표준편차   * [[: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   * [[:Degrees of Freedom]] N-1
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 와 같다. 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.  라고 할 수 있다. 
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 이때,  이때, 
  
-$$+$$ 
 \begin{align*} \begin{align*}
 E[S_k] & = E[X_1 + X_2 + . . . +X_k] \\ E[S_k] & = E[X_1 + X_2 + . . . +X_k] \\
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 $$ $$
    
-$$+$$ 
 \begin{align*} \begin{align*}
 Var[S_k] & = Var[X_1 + X_2 + . . . +X_k]  \\ Var[S_k] & = Var[X_1 + X_2 + . . . +X_k]  \\
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 이다. 이다.
  
-그렇다면, $A_k$ 에 관한 기대값과 분산값은: +그렇다면, $ A_k $ 에 관한 기대값과 분산값은: 
  
-$$+$$ 
 \begin{align*} \begin{align*}
 E[A_k] & = E[\frac{S_k}{k}] \\ E[A_k] & = E[\frac{S_k}{k}] \\
c/ms/2017/schedule/week03.txt · Last modified: 2022/05/15 11:25 by hkimscil

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