Statistik Deskriptif II:
Visualisasi & Distribusi Data

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats

# Atur gaya visualisasi agar lebih cantik
sns.set_theme(style="darkgrid", palette="muted")
plt.rcParams['figure.figsize'] = (10, 6)

# Dataset: nilai mahasiswa dari 3 kelas berbeda
np.random.seed(42)
kelas_a = np.random.normal(loc=75, scale=8, size=50)   # distribusi normal
kelas_b = np.random.exponential(scale=15, size=50) + 50 # skewed right
kelas_c = 100 - np.random.exponential(scale=10, size=50)  # skewed left

df = pd.DataFrame({
    'Nilai': np.concatenate([kelas_a, kelas_b, kelas_c]),
    'Kelas': ['A']*50 + ['B']*50 + ['C']*50
})
df['Nilai'] = df['Nilai'].clip(0, 100)  # batasi 0-100

fig, axes = plt.subplots(1, 3, figsize=(15, 5))
judul = ['Kelas A (Normal/Simetris)', 
         'Kelas B (Skewed Right +)', 
         'Kelas C (Skewed Left −)']
data_list = [kelas_a, kelas_b, kelas_c]
warna = ['#3B82F6', '#F59E0B', '#8B5CF6']

for i, (ax, data, title, color) in enumerate(zip(axes, data_list, judul, warna)):
    ax.hist(data, bins=15, color=color, alpha=0.8, edgecolor='white')
    ax.axvline(np.mean(data), color='red', linestyle='--', label=f'Mean={np.mean(data):.1f}')
    ax.axvline(np.median(data), color='green', linestyle='-', label=f'Median={np.median(data):.1f}')
    ax.set_title(title, fontsize=11)
    ax.set_xlabel('Nilai')
    ax.set_ylabel('Frekuensi')
    ax.legend(fontsize=9)
    
    # Hitung dan tampilkan skewness
    skew = stats.skew(data)
    ax.text(0.05, 0.95, f'Skewness: {skew:.2f}',
           transform=ax.transAxes, verticalalignment='top',
           bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))

plt.tight_layout()
plt.savefig('histogram_distribusi.png', dpi=150)
plt.show()

plt.figure(figsize=(10, 6))

# Boxplot dengan Seaborn (lebih cantik)
sns.boxplot(data=df, x='Kelas', y='Nilai', 
            palette=['#3B82F6', '#F59E0B', '#8B5CF6'],
            width=0.5)

# Tambahkan titik data asli (strip plot)
sns.stripplot(data=df, x='Kelas', y='Nilai', 
             color='white', alpha=0.4, size=4, jitter=True)

plt.title('Boxplot Perbandingan Nilai Tiga Kelas', fontsize=14)
plt.xlabel('Kelas')
plt.ylabel('Nilai Ujian')

# Tambahkan anotasi penjelasan boxplot
plt.annotate('● = Outlier', xy=(0.02, 0.98), xycoords='axes fraction',
             va='top', fontsize=9, color='gray')

plt.tight_layout()
plt.show()

fig, axes = plt.subplots(1, 3, figsize=(15, 5))
kelas_names = ['Kelas A', 'Kelas B', 'Kelas C']

for ax, data, name in zip(axes, data_list, kelas_names):
    # Buat Q-Q plot
    (osm, osr), (slope, intercept, r) = stats.probplot(data, dist="norm")
    ax.scatter(osm, osr, alpha=0.7, color='#3B82F6', s=30)
    ax.plot(osm, slope * np.array(osm) + intercept, 'r-', linewidth=2)
    
    ax.set_title(f'Q-Q Plot {name}')
    ax.set_xlabel('Kuantil Teoritis (Normal)')
    ax.set_ylabel('Kuantil Data')
    
    # Uji Shapiro-Wilk (formal)
    stat_sw, p_sw = stats.shapiro(data)
    status = "NORMAL" if p_sw > 0.05 else "TIDAK NORMAL"
    ax.text(0.05, 0.95, f'Shapiro p={p_sw:.3f}\n{status}',
           transform=ax.transAxes, va='top', fontsize=9,
           bbox=dict(boxstyle='round', facecolor='#1e3a5f'))

plt.tight_layout()
plt.show()

# Buat data nilai UTS dan UAS yang berkorelasi
np.random.seed(10)
uts = np.random.normal(75, 10, 60)
uas = uts + np.random.normal(0, 8, 60)   # UAS ≈ UTS + noise
uts = np.clip(uts, 40, 100)
uas = np.clip(uas, 40, 100)

plt.figure(figsize=(8, 6))
plt.scatter(uts, uas, alpha=0.7, color='#3B82F6', s=60, edgecolors='white', linewidth=0.5)

# Tambahkan garis tren (regresi linear)
z = np.polyfit(uts, uas, 1)
p = np.poly1d(z)
x_line = np.linspace(uts.min(), uts.max(), 100)
plt.plot(x_line, p(x_line), 'r--', linewidth=2, label='Garis Tren')

plt.title('Scatter Plot: Nilai UTS vs UAS')
plt.xlabel('Nilai UTS')
plt.ylabel('Nilai UAS')
plt.legend()

# Korelasi Pearson
r, p_val = stats.pearsonr(uts, uas)
plt.annotate(f'r = {r:.2f} (korelasi positif kuat)', 
             xy=(0.05, 0.92), xycoords='axes fraction', fontsize=10)

plt.tight_layout()
plt.show()