Histograms: Distribution, Density & Binning Architecture

import matplotlib.pyplot as plt
import numpy as np

# 1. Instantiate explicit Figure and Axes
fig, ax = plt.subplots(figsize=(10, 5.5), dpi=100)

# 2. Draw Histogram and capture the 3 return objects
n, bins, patches = ax.hist(
    df['order_value'],
    bins=25,              # Number of equal-width bins or array of custom edges
    range=(0, 500),       # Lower and upper range boundary (ignores outliers beyond)
    density=False,        # If True, normalizes bar areas to integrate to 1.0
    cumulative=False,     # If True, each bin accumulates all preceding counts
    color='#f59e0b',      # Fill color of the bars
    edgecolor='#0f172a',  # CRITICAL: Crisp border line separating contiguous bars
    linewidth=1.2,        # Width of bin border strokes
    alpha=0.85            # Translucency for multi-cohort overlays
)

# 3. Labeling and styling
ax.set_title("Customer Order Value Distribution", fontsize=13, fontweight='bold', pad=12)
ax.set_xlabel("Order Value ($ USD)", fontsize=11)
ax.set_ylabel("Frequency (Number of Orders)", fontsize=11)
ax.grid(axis='y', linestyle='--', alpha=0.3)

plt.tight_layout()
plt.show()

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

data = np.random.normal(loc=50, scale=10, size=2000)

fig, ax = plt.subplots(figsize=(9, 5))

# 1. Plot histogram with density=True (Area integrates to 1.0)
n, bins, patches = ax.hist(data, bins=30, density=True, color='#f59e0b', alpha=0.6, edgecolor='#0f172a')

# 2. Fit and compute theoretical Gaussian curve
mu, std = norm.fit(data)
x_vals = np.linspace(bins[0], bins[-1], 200)
pdf_curve = norm.pdf(x_vals, mu, std)

# 3. Overlay continuous PDF curve on the same axes
ax.plot(x_vals, pdf_curve, color='#ef4444', linewidth=2.5, label=f'Gaussian Fit (μ={mu:.1f}, σ={std:.1f})')

ax.set_title("Probability Density Histogram with Gaussian Fit", fontweight='bold')
ax.set_ylabel("Probability Density")
ax.legend()
plt.show()

import matplotlib.pyplot as plt
import numpy as np

# API response times in milliseconds
latency = np.random.exponential(scale=80, size=5000) + 20

fig, ax = plt.subplots(figsize=(9, 5))

# Plot cumulative probability histogram
n, bins, patches = ax.hist(
    latency,
    bins=40,
    cumulative=True,     # Sums all preceding bins
    density=True,        # Y-axis scales from 0.0 (0%) to 1.0 (100%)
    color='#10b981',
    edgecolor='#064e3b',
    alpha=0.75
)

# Benchmark: 95% SLA boundary
p95 = np.percentile(latency, 95)
ax.axhline(0.95, color='#ef4444', linestyle='--', linewidth=1.8, label='95% Target')
ax.axvline(p95, color='#ef4444', linestyle='--', linewidth=1.8, label=f'P95: {p95:.1f}ms')

ax.set_title("Empirical Cumulative Distribution Function (ECDF)", fontweight='bold')
ax.set_xlabel("Request Latency (ms)")
ax.set_ylabel("Cumulative Fraction of Requests (0.0 to 1.0)")
ax.set_ylim(0, 1.05)
ax.legend(loc='lower right')
plt.show()

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
spend = np.random.exponential(scale=50, size=2500) + 10

fig, ax = plt.subplots(figsize=(10, 5))
n, bins, patches = ax.hist(spend, bins=35, color='#0284c7', edgecolor='#082f49', alpha=0.85)

# Calculate statistical benchmarks
mean_val = np.mean(spend)
median_val = np.median(spend)
p90_val = np.percentile(spend, 90)

# 1. Overlay Mean Line (Dashed Crimson)
ax.axvline(mean_val, color='#ef4444', linestyle='--', linewidth=2, label=f'Mean: ${mean_val:.2f}')

# 2. Overlay Median Line (Solid Emerald)
ax.axvline(median_val, color='#10b981', linestyle='-', linewidth=2.2, label=f'Median: ${median_val:.2f}')

# 3. Overlay 90th Percentile SLA (Dotted Amber)
ax.axvline(p90_val, color='#f59e0b', linestyle=':', linewidth=2.5, label=f'P90 SLA: ${p90_val:.2f}')

# 4. Highlight the Top 10% VIP Region with axvspan
ax.axvspan(p90_val, bins[-1], color='#f59e0b', alpha=0.15, label='VIP Tier (Top 10%)')

ax.set_title("Customer Spend Distribution with Key Benchmarks", fontsize=13, fontweight='bold')
ax.set_xlabel("Spend ($ USD)")
ax.set_ylabel("Customer Count")
ax.legend(loc='upper right')
plt.show()

import seaborn as sns
import matplotlib.pyplot as plt

tips = sns.load_dataset("tips")

fig, ax = plt.subplots(figsize=(9, 5))

# Seaborn automated statistical distribution
sns.histplot(
    data=tips,
    x="total_bill",
    hue="time",           # Segmentation by Lunch vs. Dinner
    kde=True,             # Automatically computes and overlays KDE curve
    bins="auto",          # Intelligent FD / Sturges calculation
    stat="density",       # Normalized probability density
    common_norm=False,    # Normalizes each cohort independently
    palette={"Lunch": "#06b6d4", "Dinner": "#f59e0b"},
    alpha=0.45,
    ax=ax
)

ax.set_title("Bill Size Distribution: Lunch vs. Dinner", fontweight='bold')
plt.show()

import matplotlib.pyplot as plt
import numpy as np

# Synthetic Black Friday incident telemetry (N=10,000)
np.random.seed(42)
cache_hits = np.random.normal(32, 6, 8200)
db_lockouts = np.random.normal(890, 140, 1800)
latency = np.concatenate([cache_hits, db_lockouts])

fig, ax = plt.subplots(figsize=(10, 5.5), dpi=100)

# Render histogram
n, bins, patches = ax.hist(
    latency,
    bins=45,
    range=(0, 1400),
    color='#0284c7',
    edgecolor='#082f49',
    linewidth=1.1,
    alpha=0.85
)

# Color-code failure zone (>= 400ms) in crimson red
for p, b_left in zip(patches, bins[:-1]):
    if b_left >= 400:
        p.set_facecolor('#ef4444')

# Vertical indicators
ax.axvline(250, color='#fbbf24', linestyle='--', linewidth=2.5, label='Contractual SLA (250ms)')
ax.axvline(np.mean(latency), color='#38bdf8', linestyle=':', linewidth=2, label=f'Mean: {np.mean(latency):.1f}ms')
ax.axvline(np.median(latency), color='#10b981', linestyle='-', linewidth=2, label=f'Median: {np.median(latency):.1f}ms')

ax.set_title("Black Friday Latency Incident: Bimodal Failure Distribution", fontweight='bold')
ax.set_xlabel("Checkout Request Latency (Milliseconds)")
ax.set_ylabel("Number of Customers")
ax.legend(loc='upper right')
plt.show()