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# ==============================================================================
# TEMPLATE JAWABAN KUIS
# Komputasi Statistika, Kelas D
# Prodi S1 Statistika FSAD ITS - Semester Genap 2025/2026
# Kamis, 12 Maret 2026
# ==============================================================================
# Nama  : ___________________________
# NRP   : ___________________________
# Kelas : ___________________________
# ==============================================================================


# ==============================================================================
# Soal 1 [TOTAL 50 poin] - Winsorized Mean
# ==============================================================================

# Data
x <- c(12, 45, 52, 58, 61, 63, 67, 70, 72, 75, 78, 82, 88, 95, 310)

# --- [a] Buatlah fungsi winsorized_mean(x, alpha) ---

winsorized_mean <- function(x, alpha) {
  x_sort <- sort(x)
  n <- length(x)
  k <- floor(n*alpha)
  y <- x_sort
  
  if (k>0){
    y[1:k] <- x_sort[k +1]
    y[(n-k+1):n] <- x_sort[n-k]
  }
  return(mean(y))
  
}

# --- [b] Hitung ordinary mean (alpha=0) dan Winsorized mean 20% (alpha=0.2) ---

# Ordinary mean
ordinary_mean0 <- winsorized_mean(x, 0)
cat("Ordinary mean alpha = 0: ", ordinary_mean0, "\n")

## Ordinary mean alpha = 0:  81.86667

# Winsorized mean 20%
ordinary_mean20 <- winsorized_mean(x, 0.2)
cat("Ordinary mean 20% alpha = 0.2: ", ordinary_mean20, "\n")

## Ordinary mean 20% alpha = 0.2:  69.73333

# ==============================================================================
# Soal 2 [TOTAL 60 poin] - Weighted Multivariate Descriptive Statistics
# ==============================================================================

# --- Baca data CSV ---
df <- read.csv("C:/Users/ASRUL SANI/Downloads/Quiz 1 Komstat/data_quiz1.csv")
X <- as.matrix(df[, c("x1", "x2", "x3")])
w <- df$w

# --- [a] Buatlah fungsi weighted_corr(X, w) ---

weighted_corr <- function(X, w) {
  X <- as.matrix(X)
  n <- nrow(X)
  p <- ncol(X)
  
  W <- diag(w)
  nw <- sum(w)
  ones <- rep(1, n)
  
  x_bar_w <- (1/nw) * t(X) %*% W %*% ones
  D <- X - (ones %*% t(x_bar_w))
  Sw <- (1/nw) * t(D) %*% W %*% D
  sw <- sqrt(diag(Sw))
  V_inv <- diag(1/sw)
  Rw <-  V_inv %*% Sw %*% V_inv
  
  return(list(
    W = W,
    x_bar_w = x_bar_w,
    S_w = Sw,
    s_w = sw,
    R_w = Rw
  ))
}

# --- [b] Aplikasikan fungsi pada data ---

# Panggil fungsi
hasil <- weighted_corr(X,w)


# Tampilkan vektor mean tertimbang
print("Vektor Mean Tertimbang (x_bar_w):")

## [1] "Vektor Mean Tertimbang (x_bar_w):"

hasil$x_bar_w

##        [,1]
## x1 73.88530
## x2 65.39059
## x3 17.00938

# Tampilkan matriks varians-kovarians tertimbang
print("Matriks Korelasi Tertimbang (Sw):")

## [1] "Matriks Korelasi Tertimbang (Sw):"

hasil$S_w

##           x1        x2        x3
## x1  38.16362 -37.75105 -27.15386
## x2 -37.75105  41.10767  29.16587
## x3 -27.15386  29.16587  21.14757

# Tampilkan vektor standar deviasi tertimbang
print("Matriks Korelasi Tertimbang (sw):")

## [1] "Matriks Korelasi Tertimbang (sw):"

hasil$s_w

##       x1       x2       x3 
## 6.177671 6.411527 4.598649

# Tampilkan matriks korelasi tertimbang
print("Matriks Korelasi Tertimbang (Rw):")

## [1] "Matriks Korelasi Tertimbang (Rw):"

hasil$R_w

##            [,1]       [,2]       [,3]
## [1,]  1.0000000 -0.9531095 -0.9558207
## [2,] -0.9531095  1.0000000  0.9891979
## [3,] -0.9558207  0.9891979  1.0000000

boxplot(x,
        main = "boxplot distribusi data x",
        ylab = "Nilai",
        col = "pink",
        border = "darkred",
        pch = 19,
        cex = 1.2,
        horizontal = FALSE)

data_plot <- df[, c("x1", "x2", "x3")]

pairs(data_plot,
      main = "Matriks Scatter Plot",
      pch = 19,
      col = "brown")

hist(df$x1,
     main = "Histogram x1",
     xlab = "Data x1",
     col = "navyblue",
     border = "black",
     breaks = 10)

hist(df$x2,
     main = "Histogram x2",
     xlab = "Data x2",
     col = "skyblue",
     border = "black",
     breaks = 10)

hist(df$x3,
     main = "Histogram x3",
     xlab = "Data x3",
     col = "lightblue",
     border = "black",
     breaks = 10)

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