ALGORITMA DAN STRUKTUR DATA

TUGAS 5

Email             : brigita.melantika@student.matanauniversity.ac.id
RPubs            : https://rpubs.com/brigitatiaraem/
Jurusan          : Statistika
Address         : ARA Center, Matana University Tower
                         Jl. CBD Barat Kav, RT.1, Curug Sangereng, Kelapa Dua, Tangerang, Banten 15810.

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1 SOAL

Buatlah fungsi dengan bahasa pemrograman R untuk menghitung:

1. Intergral Tentu dan Tak Tentu

2. Luas Lingkaran, Keliling Lingkaran, dan, Volume Bola.

3. Nilai Maksimum, Minimum, Rata-rata, Median, Mode, Variansi, Standard Deviasi pada data berfrekuensi.

Jawaban:

1.1 Intergral Tentu dan Tak Tentu

library('pracma')
pracma=integral(function(x)(2*(x)^2)+6*(x)+3,
          xmin=1, xmax=5, method="Simpson",
          reltol = 1e-8)
library(mosaicCalc)

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

## The following object is masked from 'package:pracma':
## 
##     logit

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
## 
##     D

I = antiD(3*x^3+9 ~ x)
I

## function (x, C = 0) 
## 3/4 * x^4 + 9 * x + C

print(pracma)

## [1] 166.6667

1.2 Luas Lingkaran, Keliling Lingkaran, dan, Volume Bola.

phi = 3.14
r=21
data<- function(phi,r)
  
{luas = phi*r^2
  keliling = 2*phi*r
  volume =round(4/3*phi*r^3, digits = 2)

return(cat(c("luaslingkaran :", luas,
             "kelilinglingkaran :", keliling,
             "volumebola :", volume)))
}
data(phi = 3.14, r=21)

## luaslingkaran : 1384.74 kelilinglingkaran : 131.88 volumebola : 38772.72

1.3 Nilai Maksimum, Minimum, Rata-rata, Median, Mode, Variansi, Standard Deviasi pada data berfrekuensi.

Nilai = c(75,80,85,90,95,100)
Frekuensi = c(2,3,1,2,3,4)
df=data.frame(Nilai,
                Frekuensi)

df

##   Nilai Frekuensi
## 1    75         2
## 2    80         3
## 3    85         1
## 4    90         2
## 5    95         3
## 6   100         4

1.4 Nilai Max, Nilai Min, dan Mean

data = function(x,Frekuensi)
{maksimum = {
  DataUtama<-(sort(x,decreasing = F))
  tail(DataUtama, n=1)}
minimum = tail(DataUtama, n=1)
mean=round(sum(x*Frekuensi)/sum(Frekuensi), digits=2)
median<-{
totalfrekuensi<-sum(Frekuensi)
data<-sort(rep.int(x,Frekuensi))
ifelse(totalfrekuensi%%2==0,
       median<-((data[totalfrekuensi%/%2]/2) + (data[totalfrekuensi%/%2]+1)/2),
        ifelse(totalfrekuensi%%2==1,                                        median<-((data[totalfrekuensi%/%2]))))}
  modus<-{
    jabar<-sort(rep.int(x,Frekuensi))
    nilai<-unique(jabar)
    tab<-tabulate(match(jabar, nilai))
    nilai[tab==max(tab)]
}
  xbar=sum(Nilai*Frekuensi)/(sum(Frekuensi))
  xmin.xbar=(Nilai-xbar)^2
  frekuensirata=sum(Frekuensi*xmin.xbar)
  var<-frekuensirata/sum(Frekuensi)
  sd<-sqrt(var)
  return (cat(c("Nilai Maks :", maksimum,
                "Nilai min :", minimum,
                "Mean :", mean,
                "Modus :", modus,
                "Variansi :", var,
                "Standar Deviasi :", sd)))
}
data(df$Nilai,df$Frekuensi)

## Nilai Maks : 100 Nilai min : 100 Mean : 89.33 Modus : 100 Variansi : 82.8888888888889 Standar Deviasi : 9.10433352249844