Nama Anggota :

1. Muhammad Syakir Afif (2502056013)

2. Nur Arifudin (2502056016)

3. Jamilla Fatihatul Fuadiyah (2502056046)

4. Safira Hazrati Zharfa (2502056029)

5. Tirza Abigail Theodora (2502056040)

BAB 4

UKURAN GEJALA PUSAT, LETAK, PENCARAN, KEMIRINGAN DAN KERUNCINGAN

1. Ukuran Gejala Pusat

Data

data1=c(1,2,3,4,5,6,7,8,9,10,11,11,12,13,14,15,16,17,18)

Jumlah Keseluruhan Nilai

sum(data1)
## [1] 182

Rata-Rata Aritmatik

mean(data1)
## [1] 9.578947

Modus

table(data1)
## data1
##  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 
##  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1

Median

median(data1)
## [1] 10

2. Ukuran Letak

Kuartil

quantile(data1)
##   0%  25%  50%  75% 100% 
##  1.0  5.5 10.0 13.5 18.0

Desil

quantile(data1,
         probs=c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9))
##  10%  20%  30%  40%  50%  60%  70%  80%  90% 
##  2.8  4.6  6.4  8.2 10.0 11.0 12.6 14.4 16.2

3. Ukuran Pencaran atau Dispersi atau Sebaran

Data

data2=c(
10,20,30,40,50,
10,30,30,40,50,
10,30,30,40,50,
20,30,30,50
)

data2
##  [1] 10 20 30 40 50 10 30 30 40 50 10 30 30 40 50 20 30 30 50

Nilai Minimum

min(data2)
## [1] 10

Nilai Maksimum

max(data2)
## [1] 50

Range

max(data2)-min(data2)
## [1] 40

Variance

var(data2)
## [1] 180.7018

Standar Deviasi

sd(data2)
## [1] 13.44254

4. Ukuran Kemiringan (Skewness)

Data

data1=c(1,2,3,4,5,6,7,8,9,10,11,11,12,13,14,15,16,17,18)

data1
##  [1]  1  2  3  4  5  6  7  8  9 10 11 11 12 13 14 15 16 17 18

5. Ukuran Keruncingan (Kurtosis)

Aplikasi dalam R

Data 4.1

data4.1=data.frame(
  data1=c(
    1,2,3,4,5,6,7,8,9,10,
    11,11,12,13,14,15,16,17,18
  ),
  
  data2=c(
    10,10,10,20,20,30,30,30,30,30,
    30,40,40,40,40,50,50,50,50
  ),
  
  data3=c(
    1,2,2,3,3,3,3,3,4,4,
    4,5,5,6,6,NA,NA,NA,NA
  )
)

write.csv(data4.1,
          "data4.1.csv",
          row.names=FALSE)
simpan=read.table("data4.1.csv",
                  header=TRUE,
                  sep=",")

simpan
data_1=simpan$data1
data_11=na.omit(data_1)

data_2=simpan$data2
data_21=na.omit(data_2)

data_3=simpan$data3
data_31=na.omit(data_3)

data_1
##  [1]  1  2  3  4  5  6  7  8  9 10 11 11 12 13 14 15 16 17 18
data_11
##  [1]  1  2  3  4  5  6  7  8  9 10 11 11 12 13 14 15 16 17 18
data_2
##  [1] 10 10 10 20 20 30 30 30 30 30 30 40 40 40 40 50 50 50 50
data_21
##  [1] 10 10 10 20 20 30 30 30 30 30 30 40 40 40 40 50 50 50 50
data_3
##  [1]  1  2  2  3  3  3  3  3  4  4  4  5  5  6  6 NA NA NA NA
data_31
##  [1] 1 2 2 3 3 3 3 3 4 4 4 5 5 6 6
## attr(,"na.action")
## [1] 16 17 18 19
## attr(,"class")
## [1] "omit"

Menggunakan package psych

library(psych)

describe(data_11)
describe(data_21)
describe(data_31)

Menggunakan package pastecs

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 
##  610.0000000   30.0000000   32.1052632    3.1137262    6.5416960  184.2105263 
##      std.dev     coef.var 
##   13.5724179    0.4227474
stat.desc(data_31)

Aplikasi dalam R (Data Berkelompok)

Data 4.2

data4.2=data.frame(
  jurusan.angka=c(
    1,1,1,1,1,1,
    2,2,2,2,2,2
  ),
  
  jurusan.label=c(
    "matematika","matematika","matematika",
    "matematika","matematika","matematika",
    "statistika","statistika","statistika",
    "statistika","statistika","statistika"
  ),
  
  jenis.angka=c(
    1,1,1,2,2,2,
    1,1,1,2,2,2
  ),
  
  jenis.label=c(
    "laki-laki","laki-laki","laki-laki",
    "perempuan","perempuan","perempuan",
    "laki-laki","laki-laki","laki-laki",
    "perempuan","perempuan","perempuan"
  ),
  
  IQ=c(
    101,104,102,111,101,105,
    104,103,104,102,101,101
  ),
  
  EQ=c(
    102,104,104,105,106,102,
    101,112,104,101,102,104
  )
)

write.csv(data4.2,
          "data4.2.csv",
          row.names=FALSE)

Kode R

simpan=read.table("data4.2.csv",
                  header=TRUE,
                  sep=",")

simpan

Menggunakan package psych

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  104 3.79    103     104 2.97 101 111    10 0.86    -0.93 1.55
## ------------------------------------------------------------ 
## 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  104 3.79    103     104 2.97 101 111    10 0.86    -0.93 1.55
## ------------------------------------------------------------ 
## 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 6 103.83 1.6    104  103.83 2.22 102 106     4 -0.02    -1.82 0.65
## ------------------------------------------------------------ 
## 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 6 103.83 1.6    104  103.83 2.22 102 106     4 -0.02    -1.82 0.65
## ------------------------------------------------------------ 
## 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

Menggunakan package doBy

library(doBy)

summaryBy(
  IQ + EQ ~ jurusan.label + jenis.label,
  data=simpan,
  FUN=function(x) {
    c(
      ratarata=mean(x),
      standar_deviasi=sd(x),
      jumlah=sum(x)
    )
  }
)

Kesimpulan

BAB 4 membahas ukuran gejala pusat, ukuran letak, ukuran pencaran atau dispersi, ukuran kemiringan, dan ukuran keruncingan. Pada bagian aplikasi dalam R, data dianalisis menggunakan package psych, pastecs, dan doBy untuk memperoleh berbagai ukuran statistik dari data tunggal maupun data berkelompok.