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--- b:head_first_statistics:measuring_central_tendency [2023/09/11 08:18] – [skewedness] hkimscil
+++ b:head_first_statistics:measuring_central_tendency [2024/09/09 09:50] (current) – [mean] hkimscil
@@ Line 21: / Line 21: @@
 이것을 우리는 흔히 "무"라고 부른다.
 \begin{equation*}
-\mu = \frac{\sum\limits_{i=1}^{n} X_i}{n}
+\mu = \frac{\sum\limits_{i=1}^{N} X_i}{N}
 \end{equation*}
@@ Line 31: / Line 31: @@
 \begin{equation*}
 \begin{split}
-\mu = \frac{\sum\limits_{}^{} \text{fx}}{\sum{\text{f}}}
+\mu = \frac{\sum\limits_{}^{} \text{fx}}{\sum{\text{f.nothing}}}
     = \frac{1 \text{x} 19 + 3 \text{x} 20 + 1 \text{x} 21}{5}
 \end{split}
@@ Line 43: / Line 43: @@
 ===== skewedness =====
 <WRAP info>
+skewedness: 왜도
 {{skewedness.jpg}}
 </WRAP>
@@ Line 104: / Line 105: @@
 ==== e.g. 1 ====
-quartile 명령어는 r에서는 없다. 대신 quantile을 사용합니다. 둘은 비슷하나 quantile은 4분위 이상의 것을 한다.
+quartile 명령어는 r에서는 없다. 대신 quantile을 사용한다. 둘은 비슷하나 quantile은 4분위 이상의 것을 한다.
 R에서
@@ Line 202: / Line 203: @@
 >
 </code>
-|value | 1  | 4  | 6  | 8  | 9  | 10  | 11  | 12  |
-|freq  | 1  | 1  | 2  | 3  | 4  | 4   | 5  | 5   |
 <code>
@@ Line 215: / Line 212: @@
 <code>
 {1, 1, 1, 2, 2, 2, 2, 2, 3, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33}
+</code>
+<code>
+a <- c(1, 1, 1, 2, 2, 2, 2, 3, 3, 31, 31, 32, 32, 32, 32, 33, 33, 33)
+b <- c(1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 31, 31, 32, 32, 32, 32, 33, 33, 33)
+c <- c(1, 1, 1, 2, 2, 2, 2, 2, 3, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33)
+a
+b
+c
+length(a)
+length(b)
+length(c)
+mean(a)
+mean(b)
+mean(c)
+median(a)
+median(b)
+median(c)
+</code>
+<code>
+# output
+> a <- c(1, 1, 1, 2, 2, 2, 2, 3, 3, 31, 31, 32, 32, 32, 32, 33, 33, 33)
+> b <- c(1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 31, 31, 32, 32, 32, 32, 33, 33, 33)
+> c <- c(1, 1, 1, 2, 2, 2, 2, 2, 3, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33)
+> a
+ [1]  1  1  1  2  2  2  2  3  3 31 31 32 32 32 32 33 33 33
+> b
+ [1]  1  1  1  2  2  2  2  2  3  3 31 31 32 32 32 32 33 33 33
+> c
+ [1]  1  1  1  2  2  2  2  2  3 31 31 31 32 32 32 32 33 33 33
+> length(a)
+[1] 18
+> length(b)
+[1] 19
+> length(c)
+[1] 19
+> mean(a)
+[1] 17
+> mean(b)
+[1] 16.21053
+> mean(c)
+[1] 17.68421
+> median(a)
+[1] 17
+> median(b)
+[1] 3
+> median(c)
+[1] 31
+>
 </code>
@@ Line 222: / Line 267: @@
 <code>
 ## answer
+n <- 3+2+2 +3+4+4
+n
+mean.duckc <- 17
+median.duckc <- 17
+tot <- mean.duckc * n
+# 2 :: 4 인것은 이미 알고 있음
+known.sum <- (1*3)+(2*4)+(3*2)+(31*2)
+tot - known.sum
+# 227 = (32*4) + (33*3) 이므로
 duckc <- c(1,1,1,2,2,2,2,3,3,31,31,32,32,32,32,33,33,33)
 mean(duckc)