#Ukuran Gejala Pusat (Measure of Central Tendency)
simpan=read.table("Tabel 4.1.csv",header=TRUE, sep=";")
simpan
## Nilai Nilai.1 Nilai.2 Nilai.3 Nilai.4
## 1 1 5 9 12 16
## 2 2 6 10 13 17
## 3 3 7 11 14 18
## 4 4 8 11 15 NA
# Input data asli 1-18
nilai <- 1:18
# Keseluruhan Nilai (Sum)
sum(nilai)
## [1] 171
# Rata-rata (Mean) atau Rata-rata Hitung
mean(nilai)
## [1] 9.5
# Modus - Tidak ada (karena semua angka hanya muncul satu kali)
# Median
median(nilai)
## [1] 9.5
#Ukuran Pencaran atau Dispersi atau Sebaran
simpan=read.table("Tabel 4.2.csv",header=TRUE, sep=";")
simpan
## Data.1 X70 X70.1 X70.2 X70.3 X70.4 X.70
## 1 Data 2 50 60 70 80 90 X=70
## 2 Data 3 20 60 70 100 100 X=70
## 3 Data 4 20 20 10 100 200 X=70
simpan=read.table("Tabel 4.3.csv",header=TRUE, sep=";")
simpan
## Nilai Nilai.1 Nilai.2 Nilai.3 Nilai.4
## 1 10 20 30 40 50
## 2 10 30 30 40 50
## 3 10 30 30 40 50
## 4 20 30 30 50 NA
#Standar Deviasi
simpan=read.table("Tabel 4.4.csv",header=TRUE, sep=";")
simpan
## Data X X.1 X.2 X.3 X.4 Rata.rata Range Variance Standar.Deviasi
## 1 Data 1 70 70 70 70 70 70 0 0 0
## 2 Data 2 50 60 70 80 90 70 40 250 15,811
## 3 Data 3 20 60 70 100 100 70 80 1100 33,166
## 4 Data 4 20 20 10 100 200 70 180 6600 81,24
simpan=read.table("Tabel 4.5.csv",header=TRUE, sep=";")
simpan
## X X.1 X.2 X.3 X.4 X.5 Rata.rata Range Variance Standar.Deviasi
## 1 Data 5 13 14 15 14 15 14 2 1 1
## 2 Data 6 12 14 16 14 16 14 4 4 2
## 3 Data 7 8 14 20 14 20 14 12 36 6
simpan=read.table("Tabel 4.6.csv",header=TRUE, sep=";")
simpan
## X X.1 X.2 X.3 X.4 X.5 Rata.rata Standar.Deviasi
## 1 Data 9 14 15 16 17 18 16 1,58113883
## 2 Data 10 12 14 16 18 20 16 3,16227766
## 3 Data 11 10 13 16 19 22 16 4,74341649
## 4 Data 12 8 12 16 20 24 16 6,32455532
## 5 Data 13 6 11 16 21 26 16 7,90569415
#Koefisien Variasi (Coefficient of Variation)
simpan=read.table("Tabel 4.7.csv",header=TRUE, sep=";")
simpan
## Siswa Berat.Badan X
## 1 1 54,33 20000
## 2 2 58,89 20000
## 3 3 64,33 19000
## 4 4 54,21 20000
## 5 5 53,45 19000
## 6 Rata.rata 57,042 19600
## 7 Standar.Deviasi 4,6045554 547,722558
## 8 Koefisien.Variasi 0,080722 0,02794503
#Data yang Dibakukan (Standardized Data)
simpan=read.table("Tabel 4.8.csv",header=TRUE, sep=";")
simpan
## Siswa Berat Uang.Jajan Z.Baku Z.Uang.Jajan
## 1 1 54,33 20000 -0,588982091 0,730296743
## 2 2 58,89 20000 0,401341779 0,730296743
## 3 3 64,33 19000 1,582780781 -1,095445115
## 4 4 54,21 20000 -0,615043245 0,730296743
## 5 5 53,45 19000 -0,780097224 -1,095445115
## 6 Rata.rata 57,042 19600 0 0
## 7 Standar.Deviasi 4,604554 547,722558 1 1
## 8 Koefisien.Variasi 0,080722 0,02794503
#Ukuran Kemiringan (Skewness)
simpan=read.table("Tabel 4.9.csv",header=TRUE, sep=";")
simpan
## Nilai..X. Nilai..X..1 Nilai..X..2 Nilai..X..3
## 1 1 3 4 5
## 2 2 3 4 6
## 3 2 3 4 6
## 4 3 3 5 NA
#Ukuran Kemiringan (Skewness)
simpan=read.table("Tabel 4.11.csv",header=TRUE, sep=";")
simpan
## No Data.1 Data.2 Data.3 Data.4 Data.5
## 1 1 1 1 1 1 1
## 2 2 1 1 1 2 1
## 3 3 2 2 1 2 2
## 4 4 2 2 1 3 2
## 5 5 2 2 2 3 2
## 6 6 2 2 2 3 3
## 7 7 2 3 2 4 3
## 8 8 2 3 2 4 3
## 9 9 2 3 3 4 3
## 10 10 3 3 3 4 4
## 11 11 3 4 3 5 4
## 12 12 3 4 3 5 4
## 13 13 3 4 4 5 4
## 14 14 3 4 4 5 4
## 15 15 4 4 4 5 4
## 16 16 4 4 4 6 5
## 17 17 4 5 5 6 5
## 18 18 4 5 5 6 5
## 19 19 5 5 5 6 5
## 20 20 5 6 5 6 6
## 21 21 5 6 6 6 6
## 22 22 6 6 6 6 6
## 23 23 6 7 6 7 7
## 24 24 7 7 6 7 7
## 25 Kemiringan 0,5668 0,1545 0 -0,5668 0
## 26 Rata.rata 3,3375 3,875 3,5 4,625 4
## 27 Median 3 4 3,5 5 4
## 28 Modus 2 4 0 6 4
simpan=read.table("Tabel 4.12.csv",header=TRUE, sep=";")
simpan
## Nilai Data.1 Data.2 Data.3 Data.4 Data.5
## 1 1 2 2 4 1 2
## 2 2 7 4 4 2 3
## 3 3 5 4 4 3 4
## 4 4 4 6 4 4 6
## 5 5 3 3 4 5 4
## 6 6 2 3 4 7 3
## 7 7 1 2 0 2 2
par(mfrow = c(2, 3))
barplot(simpan$Data.1, names.arg = simpan$Nilai, main = "Data 1", xlab = "Nilai", ylab = "Frekuensi", col = "white", border = "black")
barplot(simpan$Data.2, names.arg = simpan$Nilai, main = "Data 2", xlab = "Nilai", ylab = "Frekuensi", col = "white", border = "black")
barplot(simpan$Data.3, names.arg = simpan$Nilai, main = "Data 3", xlab = "Nilai", ylab = "Frekuensi", col = "white", border = "black")
barplot(simpan$Data.4, names.arg = simpan$Nilai, main = "Data 4", xlab = "Nilai", ylab = "Frekuensi", col = "white", border = "black")
barplot(simpan$Data.5, names.arg = simpan$Nilai, main = "Data 5", xlab = "Nilai", ylab = "Frekuensi", col = "white", border = "black")
#Ukuran Keruncingan (Kurtosis)
simpan=read.table("Tabel 4.14.csv",header=TRUE, sep=";")
simpan
## No data1 data2 data3
## 1 1 1 1 1
## 2 2 1 1 1
## 3 3 1 1 2
## 4 4 1 2 2
## 5 5 2 2 2
## 6 6 2 2 2
## 7 7 2 2 2
## 8 8 2 2 2
## 9 9 3 2 2
## 10 10 3 3 2
## 11 11 3 3 3
## 12 12 3 3 3
## 13 Kurtosis -1,65 -0,85556 0,733333
simpan=read.table("Tabel 4.15.csv",header=TRUE, sep=";")
simpan
## Nilai Frekuensi X X.1
## 1 NA Data1 Data2 Data3
## 2 1 4 4 4
## 3 2 3 6 3
## 4 3 2 8 2
#Aplikasi dalam R
simpan=read.table("DataTabel 4.5.csv",header=TRUE, sep=";") #membaca data4.1
simpan
## data1 data2 data3
## 1 1 10 1
## 2 2 10 2
## 3 3 10 2
## 4 4 20 3
## 5 5 20 3
## 6 6 30 3
## 7 7 30 3
## 8 8 30 3
## 9 9 30 4
## 10 10 30 4
## 11 11 30 4
## 12 11 30 5
## 13 12 40 5
## 14 13 40 6
## 15 14 40 6
## 16 15 50 NA
## 17 16 50 NA
## 18 17 50 NA
## 19 18 50 NA
data_1=simpan$data1 #data_1 menyimpan data1
data_11 = na.omit(data_1) #data_11 menyimpan data1, tanpa NA
data_2=simpan$data2 #data_2 menyimpan data2
data_21 = na.omit(data_2) #data_21 menyimpan data2, tanpa NA
data_3= simpan$data3 #data_3 menyimpan data3
data_31 = na.omit(data_3) #data_31 menyimpan data3, tanpa NA
library(psych)
## Warning: package 'psych' was built under R version 4.5.3
describe(data_11) #menyajikan ukuran gejala pusat, letak, pencaran, kemiringan dan kurtosis untuk data1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 19 9.58 5.2 10 9.59 5.93 1 18 17 -0.04 -1.32 1.19
describe(data_21) #menyajikan ukuran gejala pusat, letak, pencaran, kemiringan dan kurtosis untuk data2
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 19 31.58 13.44 30 31.76 14.83 10 50 40 -0.14 -1.13 3.08
describe(data_31) #menyajikan ukuran gejala pusat, letak, pencaran, kemiringan dan kurtosis untuk data3
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 15 3.6 1.45 3 3.62 1.48 1 6 5 0.14 -1.01 0.38
library(pastecs)
stat.desc(data_11)
## nbr.val nbr.null nbr.na min max range
## 19.0000000 0.0000000 0.0000000 1.0000000 18.0000000 17.0000000
## sum median mean SE.mean CI.mean.0.95 var
## 182.0000000 10.0000000 9.5789474 1.1928535 2.5060921 27.0350877
## std.dev coef.var
## 5.1995276 0.5428078
stat.desc(data_21)
## nbr.val nbr.null nbr.na min max range
## 19.0000000 0.0000000 0.0000000 10.0000000 50.0000000 40.0000000
## sum median mean SE.mean CI.mean.0.95 var
## 600.0000000 30.0000000 31.5789474 3.0839291 6.4790946 180.7017544
## std.dev coef.var
## 13.4425353 0.4256803
stat.desc(data_31)
## x
## nbr.val 15.0000000
## nbr.null 0.0000000
## nbr.na 0.0000000
## min 1.0000000
## max 6.0000000
## range 5.0000000
## sum 54.0000000
## median 3.0000000
## mean 3.6000000
## SE.mean 0.3754363
## CI.mean.0.95 0.8052307
## var 2.1142857
## std.dev 1.4540584
## coef.var 0.4039051
#Aplikasi dalam R (Data Berkelompok)
simpan=read.table("DataTabel 4.14.csv",header=TRUE, sep=";") #membaca data4.14
simpan
## jurusan.angka jurusan.label jenis.angka jenis.label IQ EQ
## 1 1 matematika 1 laki-laki 101 102
## 2 1 matematika 1 laki-laki 104 104
## 3 1 matematika 1 laki-laki 102 104
## 4 1 matematika 2 perempuan 111 105
## 5 1 matematika 2 perempuan 101 105
## 6 1 matematika 2 perempuan 101 106
## 7 2 statistika 1 laki-laki 104 101
## 8 2 statistika 1 laki-laki 103 112
## 9 2 statistika 1 laki-laki 104 104
## 10 2 statistika 2 perempuan 102 101
## 11 2 statistika 2 perempuan 101 102
## 12 2 statistika 2 perempuan 101 104
library(psych)
describeBy(simpan$IQ, simpan$jurusan.angka)
##
## Descriptive statistics by group
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 103.33 3.93 101.5 103.33 0.74 101 111 10 1.12 -0.53 1.61
## ------------------------------------------------------------
## group: 2
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 102.5 1.38 102.5 102.5 2.22 101 104 3 0 -2.06 0.56
describeBy(simpan$IQ, simpan$jurusan.label)
##
## Descriptive statistics by group
## group: matematika
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 103.33 3.93 101.5 103.33 0.74 101 111 10 1.12 -0.53 1.61
## ------------------------------------------------------------
## group: statistika
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 102.5 1.38 102.5 102.5 2.22 101 104 3 0 -2.06 0.56
describeBy(simpan$EQ, simpan$jurusan.angka)
##
## Descriptive statistics by group
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 104.33 1.37 104.5 104.33 0.74 102 106 4 -0.49 -1.19 0.56
## ------------------------------------------------------------
## group: 2
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 104 4.15 103 104 2.22 101 112 11 1.05 -0.59 1.69
describeBy(simpan$EQ, simpan$jurusan.label)
##
## Descriptive statistics by group
## group: matematika
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 104.33 1.37 104.5 104.33 0.74 102 106 4 -0.49 -1.19 0.56
## ------------------------------------------------------------
## group: statistika
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 6 104 4.15 103 104 2.22 101 112 11 1.05 -0.59 1.69
library(doBy)
## Warning: package 'doBy' was built under R version 4.5.3
summaryBy(IQ + EQ ~ jurusan.label + jenis.label, data = simpan, FUN = function(x)
{ c(ratarata = mean(x), standar_deviasi = sd(x), jumlah=sum(x) ) } )
## jurusan.label jenis.label IQ.ratarata IQ.standar_deviasi IQ.jumlah
## 1 matematika laki-laki 102.3333 1.5275252 307
## 2 matematika perempuan 104.3333 5.7735027 313
## 3 statistika laki-laki 103.6667 0.5773503 311
## 4 statistika perempuan 101.3333 0.5773503 304
## EQ.ratarata EQ.standar_deviasi EQ.jumlah
## 1 103.3333 1.1547005 310
## 2 105.3333 0.5773503 316
## 3 105.6667 5.6862407 317
## 4 102.3333 1.5275252 307