1. Stem and Leaf Diagrams
EXAMPLE 1. 통계학 강의를 듣고 있는 30명 학생의 시험 성적은 다음과 같다.
Copy 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 :
Copy stem(x, scale = 1, width = 80, atom = 1e-08) arguments :
[Solution]
R Source Result
Copy 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)
Copy ## 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
## 10의 자리 숫자가 stem이 되고, 1의 자리 숫자가 leaf가 됨을 알 수 있다.
EXAMPLE 2. stem의 갯수를 반으로 줄여서 diagram을 그려라.
[Solution]
R Source Result
Copy 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
Copy ## The decimal point is 1 digit(s) to the right of the |
##
## 2 | 5
## 4 | 08
## 6 | 8990013333678
## 8 | 033670002357
## 10 | 00
## 2. Frequency Histograms
stem and leaf diagram은 대규모 데이터 세트에는 적합하지 않다.
이 때 사용되는 방법이 도수 분포 이다.
Copy hist(x, main = paste("Histogram of ", xname),
xlim = range(breaks),
ylim = NULL,
xlab = xname,
ylab =
... ) arguments :
EXAMPLE 3. 이전의 stem and leaf diagram을 frequency histogram으로 그려라.
R Source Histogram
Copy 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),
) EXAMPLE 4. Using histogram()
R Source Result
Copy 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)) EXAMPLE 5. Histogram of iris
R Source 1. 2.
Copy 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])
Copy > # 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])
> 3. Relative Frequency Histogram
EXAMPLE 6. Relative Frequency Histogram of Example 3 using histogram()
R Source Result
Copy 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)) 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.
5. A Very Fine Relative Frequency Histogram
6. Frequency Table
EXAMPLE 7. Using iris data set, Find the frequency table of the 2nd column(Sepal.Width) of iris.
R Source 1. 2. 3.
Copy 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)
Copy > 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
Copy > 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
Copy > 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 8. Unstable Histogram
EXAMPLE 8. Unstable Histogram
R Source 1. 2.
Copy 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))
See : Using Histograms to Understand Your Data
9. Contingency Table (Cross table)
EXAMPLE 9. Using exa2_2 data set, Find the table of each one.
Frequency table of the 2nd column
Frequency table of the 3rd column
Contingency table of the 2nd and the 3rd columns.
R Source 1. 2. 3.
Copy 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)
Copy > # 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
##
Copy > # 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
##
Copy > # 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
> 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)。
