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--- quartile [2019/09/16 11:46] – hkimscil
+++ quartile [2023/09/11 08:42] (current) – [r method] hkimscil
@@ Line 11: / Line 11: @@
 사분범위 = (상한사분위수) - (하한사분위수)
-----
 ====== Finding lower and upper quartile ======
-===== head first =====
+===== e.g. 1, Head First method =====
+<code>> k <- c(1:8)
+> k
+[1] 1 2 3 4 5 6 7 8
+> quantile(k)
+%  25%  50%  75% 100%
+.00 2.75 4.50 6.25 8.00
+> </code>
+<code>{1, 2, 3, 4, 5, 6, 7, 8}</code>
+head first
   * 하한
     * n / 4 = ?
@@ Line 23: / Line 32: @@
     * 정수가 아니면? 올림을 한 위치 값
-<code>> k <- c(1:8)
+위의 방법으로는
-> k
-[1] 1 2 3 4 5 6 7 8
-> quantile(k)
-%  25%  50%  75% 100%
-.00 2.75 4.50 6.25 8.00
-> </code>
-그러나, 위의 방법으로는
 lower quartile: 2.5
 upper quartile: 6.5
+Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
+  * 11 / 4 = 2.75 -> 3
+  * lower quartile: 15
+  * 33 / 4 = 8.25 -> 9
+  * upper: 43
-===== Method 1 =====
-  * Use the median to divide the ordered data set into two halves.
-  * If there is an odd number of data points in the original ordered data set, do not include the median (the central value in the ordered list) in either half.
-  * If there is an even number of data points in the original ordered data set, split this data set exactly in half.
-  * The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.
-  * This rule is employed by the TI-83 calculator boxplot and "1-Var Stats" functions.
-===== Method 2 =====
+===== r method =====
+in r
+<code>
+j <- c(1,2,3,4,5)
+j <- sort(j)
+quantile(j)
+</code>
+<code>
+> j <- c(1,2,3,4,5)
+> j <- sort(j)
+> quantile(j)
+%  25%  50%  75% 100%
+    2    3    4    5
+>
+</code>
+Odd number of elements
   * Use the median to divide the ordered data set into two halves.
-  * If there are an odd number of data points in the original ordered data set, include the median (the central value in the ordered list) in both halves.
+  * If there are an odd number of data points in the original ordered data set, include the median (the central value in the ordered list) in both halves. (가운데 숫자)
-  * If there are an even number of data points in the original ordered data set, split this data set exactly in half.
-  * The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.
-  * The values found by this method are also known as "Tukey's hinges."
-Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
-|     | method 1  | method 2  |
+<code>
-| Q1  | 15        | 25.5      |
+j2 <- c(1,2,3,4,5,6)
-| Q2  | 40        | 40        |
+j2 <- sort(j2)
-| Q3  | 43        | 42.5      |
+quantile(j2)
+</code>
+<code>
+> j2 <- c(1,2,3,4,5,6)
+> j2 <- sort(j2)
+> quantile(j2)
+%  25%  50%  75% 100%
+.00 2.25 3.50 4.75 6.00
+>
+>
+</code>
+Even number of elements
+  * If there are an even number of data points in the original ordered data set, split this data set exactly in half. 즉, 3과 4의 가운데 값 (50%) = 3.5
+  * lower bound (lower quartile) 앞부분을 반으로 쪼갯을 때의 숫자 (여기서는 2) 더하기, 그 다음숫자와의 차이의 (3-2) 1/4지점 (여기서는 2 + 0.25 = 2.25) 구한다.
+  * upper bound는 뒷부분의 반인 5에서 한칸 아래의 숫자인 4 더하기, 그 다음 숫자와의 차이의 (5와 4의 차이인 1) 3/4 지점을 (여기서는 4 + 0.75 = 4.75) 구한다.
+<code>
+> j3 <- c(7, 18, 5, 9, 12, 15)
+> j3s <- sort(j3)
+> j3s
+[1]  5  7  9 12 15 18
+> quantile(j3s)
+%   25%   50%   75%  100%
+.00  7.50 10.50 14.25 18.00
+>
+</code>
+median = (9+12)/2
+the 1st quartile = 7 + (9-7)*(1/4) = 7 + 0.5 = 7.5
+the 3rd quartile = 12 + (12-9)*(3/4) = 12 + 2.25 = 14.25
-in r
-<code>> k <- c(1:8)
-> k
-[1] 1 2 3 4 5 6 7 8
-> quantile(k)
-%  25%  50%  75% 100%
-.00 2.75 4.50 6.25 8.00
-> </code>
 ----
 in r