# 2-1. Three Popular Data Displays {% file src="/files/-LyWU7s\_nplrpKj8MC7p" %} Chapter 2 (Korean) {% endfile %} {% file src="/files/-Lz9wFc-FR3QGbyye6a0" %} Chapter 2 (Chinese) {% endfile %} ## 1. Stem and Leaf Diagrams **EXAMPLE 1.** 통계학 강의를 듣고 있는 30명 학생의 시험 성적은 다음과 같다. ``` 86 80 25 77 73 76 100 90 69 93 90 83 70 73 73 70 90 83 71 95 40 58 68 69 100 78 87 97 92 73 ``` 위의 데이터를 가시화하기 위한 방법 중 하나가 **stem and leaf diagram**이다. R에서는 이러한 데이터 표현을 위해 `stem()` 함수를 사용한다. **Syntax :** ``` stem(x, scale = 1, width = 80, atom = 1e-08) ``` **arguments :** * x : 수치형 벡터 * scale = : 플롯의 길이를 제어 * width = : 원하는 플롯의 넓이 * atom = : tolerance **\[Solution]** {% tabs %} {% tab title="R Source" %} ``` score <- c(86, 80, 25, 77, 73, 76, 100, 90, 69, 93, 90, 83, 70, 73, 73, 70, 90, 83, 71, 95, 40, 58, 68, 69, 100, 78, 87, 97, 92, 73) stem(score) ``` {% endtab %} {% tab title="Result" %} ``` ## The decimal point is 1 digit(s) to the right of the | ## ## 2 | 5 ## 3 | ## 4 | 0 ## 5 | 8 ## 6 | 899 ## 7 | 0013333678 ## 8 | 03367 ## 9 | 0002357 ## 10 | 00 ## ``` {% endtab %} {% endtabs %} 10의 자리 숫자가 stem이 되고, 1의 자리 숫자가 leaf가 됨을 알 수 있다. **EXAMPLE 2.** stem의 갯수를 반으로 줄여서 diagram을 그려라. **\[Solution]** {% tabs %} {% tab title="R Source" %} ``` score <- c(86, 80, 25, 77, 73, 76, 100, 90, 69, 93, 90, 83, 70, 73, 73, 70, 90, 83, 71, 95, 40, 58, 68, 69, 100, 78, 87, 97, 92, 73) stem(score, scale = 0.5) # stem의 갯수를 50%로 줄임 -> 2, 4, 6, 8, 10 등 ``` {% endtab %} {% tab title="Result" %} ``` ## The decimal point is 1 digit(s) to the right of the | ## ## 2 | 5 ## 4 | 08 ## 6 | 8990013333678 ## 8 | 033670002357 ## 10 | 00 ## ``` {% endtab %} {% endtabs %} ## 2. Frequency Histograms stem and leaf diagram은 대규모 데이터 세트에는 적합하지 않다. 이 때 사용되는 방법이 **도수 분포**이다. ``` hist(x, main = paste("Histogram of ", xname), xlim = range(breaks), ylim = NULL, xlab = xname, ylab = ... ) ``` **arguments :** * `x` : 히스토그램의 벡터 데이터 * `main =` : 히스토그램의 제목 * `xlim =` : x 축의 범위 * `ylim =` : y 축의 범위 * `xlab =` : x 축의 제목 * `ylab =` : y 축의 제목 **EXAMPLE 3.** 이전의 stem and leaf diagram을 frequency histogram으로 그려라. {% tabs %} {% tab title="R Source" %} ``` score <- c(86, 80, 25, 77, 73, 76, 100, 90, 69, 93, 90, 83, 70, 73, 73, 70, 90, 83, 71, 95, 40, 58, 68, 69, 100, 78, 87, 97, 92, 73) hist(score, xlim = c(0, 110), ylim = c(0, 12), ) ``` {% endtab %} {% tab title="Histogram" %} ![](/files/-LrM-bErW9fQBSKNJejN) {% endtab %} {% endtabs %} **EXAMPLE 4. Using `histogram()`** {% tabs %} {% tab title="R Source" %} ``` require(lattice) require(openintro) score <- c(86, 80, 25, 77, 73, 76, 100, 90, 69, 93, 90, 83, 70, 73, 73, 70, 90, 83, 71, 95, 40, 58, 68, 69, 100, 78, 87, 97, 92, 73) histogram(score, type = "count", xlim = c(0, 110), ylim = c(0, 12), breaks = seq(5, 105, by=10)) ``` {% endtab %} {% tab title="Result" %} ![](/files/-LqsJLbXZBDunZvqKO0c) {% endtab %} {% endtabs %} **EXAMPLE 5.** Histogram of `iris` {% tabs %} {% tab title="R Source" %} ``` str(iris) # iris is a dataset # partitioning of Graphic Display, 2 by 2 par(mfrow = c(2,2)) # 1. Drawing Histograms for (k in 1:4) hist(iris[[k]]) # 2. Redrawing the Histograms # 2-1) Making Main Title of the Histogram title <- paste0("Histogram of ", colnames(iris[1:4])) ; title # 2-2) Color col <- c("yellow", "lightgreen", "lightpink", "skyblue"); col # 2-3) Redrawing for (k in 1:4) hist(iris[[k]], main=title[k], xlab=colnames(iris[k]), ylab="Frequency", col = col[k]) ``` {% endtab %} {% tab title="1." %} ![](/files/-LrLy7_oNMqiHQeYuCI1) {% endtab %} {% tab title="2." %} ``` > # 2. Redrawing the Histograms > > # 2-1) Making Main Title of the Histogram > title <- paste0("Histogram of ", colnames(iris[1:4])) ; title ## [1] "Histogram of Sepal.Length" "Histogram of Sepal.Width" ## [3] "Histogram of Petal.Length" "Histogram of Petal.Width" > > # 2-2) Color > col <- c("yellow", "lightgreen", "lightpink", "skyblue"); col ## [1] "yellow" "lightgreen" "lightpink" "skyblue" > > # 2-3) Redrawing > for (k in 1:4) hist(iris[[k]], ## + main=title[k], ## + xlab=colnames(iris[k]), ## + ylab="Frequency", ## + col = col[k]) > ``` ![](/files/-LrLyOVEhJGfbXhR2Dq4) {% endtab %} {% endtabs %} ## 3. Relative Frequency Histogram **EXAMPLE 6.** Relative Frequency Histogram of Example 3 using `histogram()` {% tabs %} {% tab title="R Source" %} ``` require(lattice) require(openintro) score <- c(86, 80, 25, 77, 73, 76, 100, 90, 69, 93, 90, 83, 70, 73, 73, 70, 90, 83, 71, 95, 40, 58, 68, 69, 100, 78, 87, 97, 92, 73) histogram(score, type = "percent", xlim = c(0, 110), ylim = c(0, 40), breaks = seq(5, 105, by=10)) ``` {% endtab %} {% tab title="Result" %} ![](/files/-LqsJ4S4X-VHipyC2BeU) {% endtab %} {% endtabs %} **Note :** y 축의 값이 갯수(count)가 아닌 백분율(percent)로 출력된다. ## 4. Sample size and Relative Frequency Histograms sample size가 커짐에 따라 전체 모양은 좌우 대칭의 종 모양이 된다. ![](/files/-LqsJxLJ3Ulzb8UG8CXs) ## 5. A Very Fine Relative Frequency Histogram ![](/files/-LqsK1MNnT2ijKKLGw1H) ### ## 6. Frequency Table **EXAMPLE 7.** Using `iris` data set, Find the frequency table of the 2nd column(`Sepal.Width`) of `iris`. {% tabs %} {% tab title="R Source" %} ``` library(Rstat) # import iris data set data(iris) # data structure of iris str(iris) # select the 2nd column x <- iris[[2]] # 1. frequency table freq.table(x) # 2. frequenct table & the yellow histogram freq.table(x, mp=TRUE, col=7) # 3. Change the class interval as 0.5 (mycut <- seq(2, 4.5, by=0.5)) freq.table(x, cut=mycut) freq.table(x, cut=mycut, mp=TRUE, col=0) ``` {% endtab %} {% tab title="1." %} ``` > freq.table(x) ## Center Freq Cum-Fr Rel-Fr Rel-CFr ## (2, 2.2] 2.1 4 4 0.0267 0.0267 ## (2.2, 2.4] 2.3 7 11 0.0467 0.0733 ## (2.4, 2.6] 2.5 13 24 0.0867 0.1600 ## (2.6, 2.8] 2.7 23 47 0.1533 0.3133 ## (2.8, 3] 2.9 36 83 0.2400 0.5533 ## (3, 3.2] 3.1 24 107 0.1600 0.7133 ## (3.2, 3.4] 3.3 18 125 0.1200 0.8333 ## (3.4, 3.6] 3.5 10 135 0.0667 0.9000 ## (3.6, 3.8] 3.7 9 144 0.0600 0.9600 ## (3.8, 4] 3.9 3 147 0.0200 0.9800 ## (4, 4.2] 4.1 2 149 0.0133 0.9933 ## (4.2, 4.4] 4.3 1 150 0.0067 1.0000 ``` {% endtab %} {% tab title="2." %} ``` > freq.table(x, mp=TRUE, col=7) Center Freq Cum-Fr Rel-Fr Rel-CFr (2, 2.2] 2.1 4 4 0.0267 0.0267 (2.2, 2.4] 2.3 7 11 0.0467 0.0733 (2.4, 2.6] 2.5 13 24 0.0867 0.1600 (2.6, 2.8] 2.7 23 47 0.1533 0.3133 (2.8, 3] 2.9 36 83 0.2400 0.5533 (3, 3.2] 3.1 24 107 0.1600 0.7133 (3.2, 3.4] 3.3 18 125 0.1200 0.8333 (3.4, 3.6] 3.5 10 135 0.0667 0.9000 (3.6, 3.8] 3.7 9 144 0.0600 0.9600 (3.8, 4] 3.9 3 147 0.0200 0.9800 (4, 4.2] 4.1 2 149 0.0133 0.9933 (4.2, 4.4] 4.3 1 150 0.0067 1.0000 ``` ![](/files/-LrLoXROVlF98YASmkFA) {% endtab %} {% tab title="3." %} ``` > freq.table(x, cut=mycut, mp=TRUE, col=4) ## Center Freq Cum-Fr Rel-Fr Rel-CFr ## (2, 2.5] 2.25 19 19 0.1267 0.1267 ## (2.5, 3] 2.75 64 83 0.4267 0.5533 ## (3, 3.5] 3.25 48 131 0.3200 0.8733 ## (3.5, 4] 3.75 16 147 0.1067 0.9800 ## (4, 4.5] 4.25 3 150 0.0200 1.0000 ``` ![](/files/-LrLoqbl_2x1qg15_n9i) {% endtab %} {% endtabs %} ## 8. Unstable Histogram * Type-A : Isolated Island * Type-B : Multimodal * Type-C : Outliers * Type-D : Cliff **EXAMPLE 8.** Unstable Histogram {% tabs %} {% tab title="R Source" %} ``` library(Rstat) # 1. Types of Unstable Histogram unstable.hist() # refer to ch2.man(2) # 2. Changing the Parameters of unstable.hist() unstable.hist(N=100, m2=4, a=11, b=12, c=8, vc=rainbow(4)) ``` {% endtab %} {% tab title="1." %} ![](/files/-LrM2ZfN6XHVzKLa6tJp) {% endtab %} {% tab title="2." %} ![](/files/-LrM2dF-IESP1MMcQ-xy) {% endtab %} {% endtabs %} **See :** [Using Histograms to Understand Your Data](https://statisticsbyjim.com/basics/histograms/) ## 9. Contingency Table (Cross table) **EXAMPLE 9.** Using `exa2_2` data set, Find the table of each one. 1. Frequency table of the 2nd column 2. Frequency table of the 3rd column 3. Contingency table of the 2nd and the 3rd columns. {% tabs %} {% tab title="R Source" %} ``` library(Rstat) # data import data(exa2_2) # exa2_2 is a dataset of Rstat x <- exa2_2 str(x) # 1. Frequency table of the 2nd Column x2 <- x[[2]] ; x2 # x2 : factor variable x21 <- table(x) ; x21 # x22 <- prop.table(x21) ; round(x22,2) x23 <- addmargins(x22) ; round(x23,2) # 2. Frequency table of the 3rd column x3 <- x[[3]] ; x3 # x3 : factor variable x31 <- table(x3) ; x31 # x32 <- prop.table(x31) ; round(x32,2) x33 <- addmargins(x32) ; round(x33,2) # 3. Contingency table of the 2nd and the 3rd Columns x41 <- table(x2, x3) ; x41 x42 <- prop.table(x41) ; round(x42,2) x43 <- addmargins(x42) ; round(x43,2) ``` {% endtab %} {% tab title="1." %} ``` > # 1. Frequency table of the 2nd Column > x2 <- x[[2]] ; head(x2) # x2 : factor variable ## [1] 학생부종합 학생부종합 학생부종합 학생부교과 학생부교과 학생부종합 ## Levels: 논술우수 정시일반 학생부교과 학생부종합 > x21 <- table(x2) ; x21 # ## x2 ## 논술우수 정시일반 학생부교과 학생부종합 ## 43 87 51 29 > x22 <- prop.table(x21) ; round(x22,2) ## x2 ## 논술우수 정시일반 학생부교과 학생부종합 ## 0.20 0.41 0.24 0.14 > x23 <- addmargins(x22) ; round(x23,2) ## x2 ## 논술우수 정시일반 학생부교과 학생부종합 Sum ## 0.20 0.41 0.24 0.14 1.00 ## ``` {% endtab %} {% tab title="2." %} ``` > # 2. Frequency table of the 3rd column > x3 <- x[[3]] ; head(x3) # x3 : factor variable ## [1] 자율활동 교과활동 자율활동 교과활동 교과활동 진로활동 ## Levels: 교과활동 동아리 봉사활동 자율활동 진로활동 > x31 <- table(x3) ; x31 # ## x3 ## 교과활동 동아리 봉사활동 자율활동 진로활동 ## 86 31 9 62 22 > x32 <- prop.table(x31) ; round(x32,2) ## x3 ## 교과활동 동아리 봉사활동 자율활동 진로활동 ## 0.41 0.15 0.04 0.30 0.10 > x33 <- addmargins(x32) ; round(x33,2) ## x3 ## 교과활동 동아리 봉사활동 자율활동 진로활동 Sum ## 0.41 0.15 0.04 0.30 0.10 1.00 ## ``` {% endtab %} {% tab title="" %} ``` ``` {% endtab %} {% tab title="3." %} ``` > # 3. Contingency table of the 2nd and the 3rd Columns > x41 <- table(x2, x3) ; x41 ## x3 ## x2 교과활동 동아리 봉사활동 자율활동 진로활동 ## 논술우수 22 6 1 8 6 ## 정시일반 35 16 1 28 7 ## 학생부교과 26 5 4 13 3 ## 학생부종합 3 4 3 13 6 > x42 <- prop.table(x41) ; round(x42,2) ## x3 ## x2 교과활동 동아리 봉사활동 자율활동 진로활동 ## 논술우수 0.10 0.03 0.00 0.04 0.03 ## 정시일반 0.17 0.08 0.00 0.13 0.03 ## 학생부교과 0.12 0.02 0.02 0.06 0.01 ## 학생부종합 0.01 0.02 0.01 0.06 0.03 > x43 <- addmargins(x42) ; round(x43,2) ## x3 ## x2 교과활동 동아리 봉사활동 자율활동 진로활동 Sum ## 논술우수 0.10 0.03 0.00 0.04 0.03 0.20 ## 정시일반 0.17 0.08 0.00 0.13 0.03 0.41 ## 학생부교과 0.12 0.02 0.02 0.06 0.01 0.24 ## 학생부종합 0.01 0.02 0.01 0.06 0.03 0.14 ## Sum 0.41 0.15 0.04 0.30 0.10 1.00 > ``` {% endtab %} {% endtabs %} 1）频数(分布)表(frequency table)。\ 2）相对​频数(分布)表​(relative frequency table)。 \ 3）频数分布图(frequency diagram)。 \ 4）相对频数分布图(relative frequency diagram)。 \ 5）茎叶图(stem and leaf diagram)。 \ 6）情形分析表(contingency table)。 --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. 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