Histograms and Distribution Analysis

import matplotlib.pyplot as plt
import numpy as np
from scipy import stats

np.random.seed(42)
salaries = np.random.normal(loc=75000, scale=15000, size=1000)

fig, axes = plt.subplots(2, 2, figsize=(13, 10))

# 1: Basic histogram
axes[0,0].hist(salaries, bins=30, color='#2196F3', edgecolor='white', alpha=0.8)
axes[0,0].set_title('Basic Histogram (30 bins)')
axes[0,0].set_xlabel('Salary ($)')

# 2: Different bin sizes
axes[0,1].hist(salaries, bins=10, color='#4CAF50', edgecolor='white', alpha=0.8, label='10 bins')
axes[0,1].hist(salaries, bins=50, color='#FF9800', edgecolor='white', alpha=0.5, label='50 bins')
axes[0,1].set_title('Bin Size Comparison')
axes[0,1].legend()

# 3: Histogram + KDE
count, bins, _ = axes[1,0].hist(salaries, bins=30, color='#9C27B0',
                                  edgecolor='white', alpha=0.6, density=True)
x_range = np.linspace(salaries.min(), salaries.max(), 200)
kde = stats.gaussian_kde(salaries)
axes[1,0].plot(x_range, kde(x_range), 'r-', linewidth=2.5, label='KDE')
axes[1,0].axvline(salaries.mean(), color='blue', linestyle='--', label=f'Mean: ${salaries.mean():,.0f}')
axes[1,0].axvline(np.median(salaries), color='green', linestyle='--', label=f'Median: ${np.median(salaries):,.0f}')
axes[1,0].set_title('Histogram + KDE with Reference Lines')
axes[1,0].legend(fontsize=8)

# 4: Skewed distribution
skewed = np.random.exponential(scale=30000, size=1000) + 20000
axes[1,1].hist(skewed, bins=40, color='#F44336', edgecolor='white', alpha=0.8, density=True)
x_s = np.linspace(skewed.min(), skewed.max(), 200)
axes[1,1].plot(x_s, stats.gaussian_kde(skewed)(x_s), 'b-', linewidth=2.5)
skewness = stats.skew(skewed)
axes[1,1].set_title(f'Right-Skewed Distribution (skew={skewness:.2f})')
axes[1,1].set_xlabel('Value')

for ax in axes.flatten():
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)
    ax.grid(True, alpha=0.3)

plt.suptitle('Histogram Variations', fontsize=14, fontweight='bold')
plt.tight_layout()
plt.savefig('histograms.png', dpi=150)
plt.show()

# Compare salary distributions across departments
eng_salaries  = np.random.normal(95000, 18000, 300)
mkt_salaries  = np.random.normal(72000, 12000, 200)
sales_salaries = np.random.normal(65000, 20000, 250)

fig, ax = plt.subplots(figsize=(11, 6))

for salaries, dept, color in [(eng_salaries, 'Engineering', '#1565C0'),
                                (mkt_salaries,  'Marketing', '#2E7D32'),
                                (sales_salaries, 'Sales', '#E65100')]:
    ax.hist(salaries, bins=30, alpha=0.5, color=color, edgecolor='none', label=dept)
    ax.axvline(salaries.mean(), color=color, linestyle='--', linewidth=1.5)

ax.set_title('Salary Distribution by Department', fontsize=14, fontweight='bold')
ax.set_xlabel('Annual Salary ($)')
ax.set_ylabel('Employee Count')
ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: f'${x/1000:.0f}K'))
ax.legend(title='Department')
ax.grid(True, alpha=0.3)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
plt.tight_layout()
plt.savefig('distribution_comparison.png', dpi=150)
plt.show()