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--- variability_and_spread [2019/09/24 10:13] – hkimscil
+++ variability_and_spread [2019/09/24 13:56] – hkimscil
@@ Line 5: / Line 5: @@
 | 7  | 8  | 9  | 10  | 11  | 12  | 13  |
 | 1  | 1  | 2  | 2  | 2  | 1  | 1  |
 ^  B  ^^^^^
 | 7  | 8  | 10  | 11  | 13  |
 | 1  | 2  | 4  | 2  | 1   |
 ^  C  ^^^^^^^
 | 3  | 6  | 7  | 10  | 11  | 13  | 30  |
 | 2  | 1  | 2  | 3  | 1  | 1  | 1  |
+<code>
+a <- c(7,8,9,9,10,10,11,11,12,13)
+b <- c(7,8,8,10,10,10,10,11,11,13)
+c <- c(3,3,6,7,7,10,10,10,11,13,30)
+c <- c(3,3,6,7,7,10,11,13,15,20,30)
+data <- list(a,b,c)
+data
+sapply(data,mean)
+sapply(data,sd)
+sapply(data,var)
+</code>
+<code>
+> data
+[[1]]
+ [1]  7  8  9  9 10 10 11 11 12 13
+[[2]]
+ [1]  7  8  8 10 10 10 10 11 11 13
+[[3]]
+ [1]  3  3  6  7  7 10 10 10 11 13 30
+> sapply(data,mean)
+[1] 10.0  9.8 10.0
+> sapply(data,sd)
+[1] 1.825742 1.751190 7.362065
+> sapply(data,var)
+[1]  3.333333  3.066667 54.200000
+</code>
 [[:range]]
@@ Line 18: / Line 55: @@
 [[:quartile]]
 [[:variance]]
-  * $ \sum \text{deviation score}^2 $
+  * $ \sum \text{deviation score}^2 = \sum \text{ds}^2 $
   * $ \sum \text{error}^2 $
@@ Line 27: / Line 64: @@
     * Sum of Square (SS)
-  * $ \sum \text{ds}^2 = \text{SS} = \text{Sum of Square} $
+  * $ \sum \text{ds}^2 = \text{SS} = \text{Sum of Square} $ (([[:regression#표준오차_잔여변량_standard_error_residual]]의 Figure 1을 보면 x와 y가 모두 숫자로 측정된 변인일 때, Y의 평균만을 사용해서 Y값을 예측했을 때는 SS<sub>total</sub>이라고 설명한다.))
   * $$ \text{variance} = \frac {SS}{n-1} = \frac {SS}{df}$$
   * calculation of variance (an easy way)
+    * $ \displaystyle \frac{\sum(X_{i})}{N} - \mu^2$
 [[:standard deviation]]
 [[:standard score]]