UTS STATISTIKA
arisna nuri salsabila
2022-10-26
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- Bangkitkan bilangan acak yang berdistribusi exponential (λ) dengan metode Inverse Transform Method, yang amatannya berjumlah 10000, dengan pdf
n <- 10000
u <- runif(n)
set.seed(10) # membuat seed
x <- -(log(1-u)/2) #log merupakan ln di R
head(x)## [1] 0.19515593 0.80926837 0.03295969 0.12159156 0.50176118 0.67455867length(x)## [1] 10000set.seed(10) # membuat seed
y <- rexp(n,rate = 3)
head(y)## [1] 0.004985469 0.306740402 0.250719646 0.525013950 0.077219539 0.362224334length(y)## [1] 10000par(mfrow=c(1,2))
hist(x,main = "Exp dari Invers transform")
hist(y,main = "Exp dari fungsi rexp")
2 A. Buatlah Digram Frame dengan menambahkan kolom baru nilai total skor
dan ratarata skor
studentperformace= read.csv("C:/Users/Hp/Downloads/StudentsPerformance.csv",header= TRUE)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6 ✔ purrr 0.3.5
## ✔ tibble 3.1.8 ✔ dplyr 1.0.10
## ✔ tidyr 1.2.1 ✔ stringr 1.4.1
## ✔ readr 2.1.3 ✔ forcats 0.5.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()head(studentperformace)## gender race.ethnicity parental.level.of.education lunch
## 1 female group B bachelor's degree standard
## 2 female group C some college standard
## 3 female group B master's degree standard
## 4 male group A associate's degree free/reduced
## 5 male group C some college standard
## 6 female group B associate's degree standard
## test.preparation.course math.score reading.score writing.score
## 1 none 72 72 74
## 2 completed 69 90 88
## 3 none 90 95 93
## 4 none 47 57 44
## 5 none 76 78 75
## 6 none 71 83 78Data.Siswa <- studentperformace%>%mutate(score.average=(math.score+reading.score+writing.score)/3,score.sum=math.score+reading.score+writing.score)
head(Data.Siswa)## gender race.ethnicity parental.level.of.education lunch
## 1 female group B bachelor's degree standard
## 2 female group C some college standard
## 3 female group B master's degree standard
## 4 male group A associate's degree free/reduced
## 5 male group C some college standard
## 6 female group B associate's degree standard
## test.preparation.course math.score reading.score writing.score score.average
## 1 none 72 72 74 72.66667
## 2 completed 69 90 88 82.33333
## 3 none 90 95 93 92.66667
## 4 none 47 57 44 49.33333
## 5 none 76 78 75 76.33333
## 6 none 71 83 78 77.33333
## score.sum
## 1 218
## 2 247
## 3 278
## 4 148
## 5 229
## 6 232tibble(Data.Siswa[1:10])## # A tibble: 1,000 × 10
## gender race.e…¹ paren…² lunch test.…³ math.…⁴ readi…⁵ writi…⁶ score…⁷ score…⁸
## <chr> <chr> <chr> <chr> <chr> <int> <int> <int> <dbl> <int>
## 1 female group B bachel… stan… none 72 72 74 72.7 218
## 2 female group C some c… stan… comple… 69 90 88 82.3 247
## 3 female group B master… stan… none 90 95 93 92.7 278
## 4 male group A associ… free… none 47 57 44 49.3 148
## 5 male group C some c… stan… none 76 78 75 76.3 229
## 6 female group B associ… stan… none 71 83 78 77.3 232
## 7 female group B some c… stan… comple… 88 95 92 91.7 275
## 8 male group B some c… free… none 40 43 39 40.7 122
## 9 male group D high s… free… comple… 64 64 67 65 195
## 10 female group B high s… free… none 38 60 50 49.3 148
## # … with 990 more rows, and abbreviated variable names ¹race.ethnicity,
## # ²parental.level.of.education, ³test.preparation.course, ⁴math.score,
## # ⁵reading.score, ⁶writing.score, ⁷score.average, ⁸score.sumB. Hitung nilai summary
summary(Data.Siswa) ## gender race.ethnicity parental.level.of.education
## Length:1000 Length:1000 Length:1000
## Class :character Class :character Class :character
## Mode :character Mode :character Mode :character
##
##
##
## lunch test.preparation.course math.score reading.score
## Length:1000 Length:1000 Min. : 0.00 Min. : 17.00
## Class :character Class :character 1st Qu.: 57.00 1st Qu.: 59.00
## Mode :character Mode :character Median : 66.00 Median : 70.00
## Mean : 66.09 Mean : 69.17
## 3rd Qu.: 77.00 3rd Qu.: 79.00
## Max. :100.00 Max. :100.00
## writing.score score.average score.sum
## Min. : 10.00 Min. : 9.00 Min. : 27.0
## 1st Qu.: 57.75 1st Qu.: 58.33 1st Qu.:175.0
## Median : 69.00 Median : 68.33 Median :205.0
## Mean : 68.05 Mean : 67.77 Mean :203.3
## 3rd Qu.: 79.00 3rd Qu.: 77.67 3rd Qu.:233.0
## Max. :100.00 Max. :100.00 Max. :300.0B. Hitung nilai skewness dan kurtosis
library(e1071)
skewness(studentperformace$math.score)## [1] -0.2780989skewness(studentperformace$reading.score)## [1] -0.2583277skewness(studentperformace$writing.score)## [1] -0.2885762kurtosis(Data.Siswa$math.score)## [1] 0.2610652kurtosis(Data.Siswa$reading.score)## [1] -0.07976785kurtosis(Data.Siswa$writing.score)## [1] -0.04511069C. Buatlah Dagram Pie Chart pada (i) gender, (ii) race.ethnicity, (iii) parental.level.of.education, (iv) lunch dan (v) test.preparation.course dengan menampilkan label persentase (%)
gender=table(studentperformace$gender)
piepercent = round(100*gender/sum(gender), 1)
pie(gender, labels = piepercent, main = "pie chart gender",col = rainbow(length(gender)))
legend("topright", c("female","male"), cex = 0.8,
fill =rainbow(length(gender)))
race.ethnicity=table(studentperformace$race.ethnicity)
piepercent = round(100*race.ethnicity/sum(race.ethnicity), 1)
pie(race.ethnicity, labels = piepercent, main = "pie chart race.ethnicity",col = rainbow(length(race.ethnicity)))
legend("topright", c("group A","group B","group C","group D","group E"), cex = 0.8,
fill =rainbow(length(race.ethnicity)))
parental.level.of.education=table(studentperformace$parental.level.of.education)
piepercent = round(100*parental.level.of.education/sum(parental.level.of.education), 1)
pie(parental.level.of.education, labels = piepercent, main = "pie chart parental.level.of.education",col = rainbow(length(parental.level.of.education)))
legend("topright", c("bachelor's","some college","master's degree","high school","associate's degree"), cex = 0.8,
fill =rainbow(length(parental.level.of.education)))
lunch=table(studentperformace$lunch)
piepercent = round(100*lunch/sum(lunch), 1)
pie(lunch, labels = piepercent, main = "pie chart lunch",col = rainbow(length(lunch)))
legend("topright", c("standard","free/reduced"), cex = 0.8,
fill =rainbow(length(lunch)))
test.preparation.course=table(studentperformace$test.preparation.course)
piepercent = round(100*test.preparation.course/sum(test.preparation.course), 1)
pie(test.preparation.course, labels = piepercent, main = "pie chart test.preparation.course",col = rainbow(length(test.preparation.course)))
legend("topright", c("none","completed"), cex = 0.8,
fill =rainbow(length(test.preparation.course)))
D. Buatlah diagram batang yang telah diurutkan pada data rata-rata skor
terhadap (i) parental.level.of.education (ii) race.ethnicity
rataan = aggregate(score.average~parental.level.of.education, data= Data.Siswa, FUN = mean)
rata= rataan[ , -1]
rate.pare= rataan[ , -2]
ggplot(rataan, aes(x = rate.pare, y = rata , fill = rata ))+geom_bar(stat = "identity")+labs(title="DIAGRAM RATA-RATA SKOR TERHADAP PARENTAL EDUCATION")
rataan = aggregate(score.average~race.ethnicity, data= Data.Siswa, FUN = mean)
rata= rataan[ , -1]
rate.pare= rataan[ , -2]
ggplot(rataan, aes(x = rate.pare, y = rata , fill = rata ))+geom_bar(stat = "identity")+labs(title="DIAGRAM RATA-RATA SKOR TERHADAP PARENTAL EDUCATION")
E. Buatlah diagram batang cluster/stacked pada, gunakan ggplot (i) parental level of education dan gender terhadap total score ; (ii) race.ethnicity dan gender terhadap total score
total.skor=c(Data.Siswa$score.sum)
ggplot(studentperformace, aes(x = parental.level.of.education, y = total.skor , fill = gender))+geom_bar(stat = "identity")+labs(title="DIAGRAM BATANG/CLUSTER")
ggplot(studentperformace, aes(x = race.ethnicity, y = total.skor , fill = gender))+geom_bar(stat = "identity")+labs(title="DIAGRAM BATANG/CLUSTER")
F. Buatlah visualisasi sebaran data skor matematika, skor writing dan
skor reading pada masing-masing jenis kelamin dengan menggunakan
histogram
#sebaran mathe.score pada masing-masing gender
group = studentperformace$gender
ggplot(studentperformace, aes(x= math.score, col = group)) + geom_histogram(fill= "light grey", alpha=0.5, position="identity")+ labs(title = "histogram math.score terhadap gender")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#sebaran reading.score pada masing-masing gender
group = studentperformace$gender
ggplot(studentperformace, aes(x= reading.score, color = group)) + geom_histogram(fill="light grey", alpha=0.5, position="identity")+ labs(title = "histrogram reading.score terhadap gender")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#sebaran reading.score pada masing-masing gender
group = studentperformace$gender
ggplot(studentperformace, aes(x= writing.score, color = group)) + geom_histogram(fill="light grey", alpha=0.5, position="identity")+ labs(title = "histogram writing.score terhadap gender")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
G. Buatlah visualisasi boxplot pada masing-masing skor kemampuan
(metamatika,writing, reading) terhadap parental education level di
masing-masing gender
ggplot(studentperformace,mapping=aes(x=parental.level.of.education, y= math.score, fill=gender))+geom_violin(fill="#2D2D2D", alpha=0.5, trim=F,width=1.00)+geom_boxplot()+ labs(title="boxplot pada skor mat terhadap parental education di masing' gender")+coord_flip()+scale_fill_brewer(palette="RdPu")
ggplot(studentperformace,mapping=aes(x=parental.level.of.education, y= writing.score, fill=gender))+geom_violin(fill="#2D2D2D", alpha=0.5, trim=F,width=1.00)+geom_boxplot()+ labs(title="boxplot pada skor menulis terhadap parental education di masing' gender")+coord_flip()+scale_fill_brewer(palette="RdPu")
ggplot(studentperformace,mapping=aes(x=parental.level.of.education, y= reading.score, fill=gender))+geom_violin(fill="#2D2D2D", alpha=0.5, trim=F,width=1.00)+geom_boxplot()+ labs(title="boxplot pada skor membaca terhadap parental education di masing' gender")+coord_flip()+scale_fill_brewer(palette="RdPu")
H. Buatlah scatter plot antara skor matematika, writing dan reading
#scatterplot antara math.score dan reading.score
plot(studentperformace$math.score,
studentperformace$reading.score, pch = 20, cex = 1, frame = FALSE, xlab = "Math Score", ylab = "Reading Score", main="Scatterplot math.score dan reading.score")
#scatterplot antara reading.score dan writing.score
plot(studentperformace$reading.score, studentperformace$writing.score, pch = 20, cex = 1, frame = FALSE, xlab = "Reading Score" , ylab = "Writing Score", main="Scatterplot Reading Score dan Writing Score")
#scatterplot antara writing.score dan math.score
plot(studentperformace$writing.score, studentperformace$math.score, pch = 20, cex = 1, frame = FALSE, xlab = "Writing Score", ylab = "Math Score", main="Scatterplot Writing Score dan Math Score")
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