Combined Visualizations¶

Combine box plots with other chart types for comprehensive data analysis and presentation.

Box Plot with Histogram¶

Pair box plots with histograms to show both summary statistics and distributional shape.

1. Side by Side Layout¶

```python import matplotlib.pyplot as plt import numpy as np

np.random.seed(42) data = np.random.normal(100, 15, 500)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))

ax1.hist(data, bins=25, edgecolor='black', alpha=0.7) ax1.axvline(np.mean(data), color='red', linestyle='--', label='Mean') ax1.axvline(np.median(data), color='blue', linestyle='--', label='Median') ax1.legend() ax1.set_title('Histogram')

ax2.boxplot(data) ax2.set_title('Box Plot')

plt.tight_layout() plt.show() ```

2. Stacked Vertically¶

```python fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 6), gridspec_kw={'height_ratios': [3, 1]})

ax1.hist(data, bins=25, edgecolor='black', alpha=0.7) ax1.set_ylabel('Frequency')

ax2.boxplot(data, vert=False) ax2.set_xlabel('Value')

plt.tight_layout() plt.show() ```

3. Reusable Function¶

```python def plot_distribution(data, title='Distribution Analysis', bins=20): mean = np.mean(data) median = np.median(data)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4))
fig.suptitle(title, fontsize=14)

ax1.hist(data, bins=bins, density=True, alpha=0.7, edgecolor='black')
ax1.axvline(mean, color='blue', linestyle='--', label=f'Mean: {mean:.1f}')
ax1.axvline(median, color='red', linestyle='--', label=f'Median: {median:.1f}')
ax1.legend()
ax1.set_title('Histogram')

ax2.boxplot(data)
ax2.set_title('Box Plot')

plt.tight_layout()
plt.show()

```

Box Plot with Reference Lines¶

Add horizontal reference lines to compare distributions against benchmarks.

1. Single Reference Line¶

```python fig, ax = plt.subplots()

data = [np.random.normal(100, 15, 100) for _ in range(4)] ax.boxplot(data, labels=['Q1', 'Q2', 'Q3', 'Q4']) ax.axhline(y=100, color='red', linestyle='--', label='Target', alpha=0.7) ax.legend() ax.set_ylabel('Performance')

plt.show() ```

2. Multiple Reference Lines¶

```python fig, ax = plt.subplots()

ax.boxplot(data, labels=['Q1', 'Q2', 'Q3', 'Q4']) ax.axhline(y=90, color='red', linestyle='--', label='Minimum', alpha=0.7) ax.axhline(y=100, color='green', linestyle='--', label='Target', alpha=0.7) ax.axhline(y=110, color='blue', linestyle='--', label='Stretch', alpha=0.7) ax.legend()

plt.show() ```

3. Shaded Region¶

```python fig, ax = plt.subplots()

ax.boxplot(data, labels=['Q1', 'Q2', 'Q3', 'Q4']) ax.axhspan(95, 105, color='green', alpha=0.2, label='Acceptable Range') ax.legend()

plt.show() ```

Box Plot with Scatter Overlay¶

Show individual data points alongside the box plot summary.

1. Jittered Points¶

```python import matplotlib.pyplot as plt import numpy as np

np.random.seed(42) data = [np.random.normal(0, std, 50) for std in range(1, 5)]

fig, ax = plt.subplots()

bp = ax.boxplot(data, patch_artist=True, showfliers=False) for patch in bp['boxes']: patch.set_facecolor('lightblue') patch.set_alpha(0.5)

for i, d in enumerate(data, 1): jitter = np.random.normal(0, 0.04, len(d)) ax.scatter(np.full_like(d, i) + jitter, d, alpha=0.5, s=20, c='steelblue')

plt.show() ```

2. Swarm-Like Layout¶

```python def add_points(ax, data, positions, width=0.2): for pos, d in zip(positions, data): n = len(d) offsets = np.linspace(-width/2, width/2, n) ax.scatter(np.full(n, pos) + offsets, np.sort(d), alpha=0.4, s=15, c='darkblue')

fig, ax = plt.subplots() bp = ax.boxplot(data, showfliers=False) add_points(ax, data, range(1, len(data) + 1)) plt.show() ```

3. Strip Plot Style¶

```python fig, ax = plt.subplots()

ax.boxplot(data, showfliers=False, widths=0.3)

for i, d in enumerate(data, 1): y = d x = np.random.uniform(i - 0.15, i + 0.15, len(d)) ax.scatter(x, y, alpha=0.3, s=10, c='black')

plt.show() ```

Grouped Box Plots¶

Compare multiple categories across groups.

1. Manual Positioning¶

```python import matplotlib.pyplot as plt import numpy as np

np.random.seed(42)

group1_a = np.random.normal(100, 10, 50) group1_b = np.random.normal(110, 15, 50) group2_a = np.random.normal(90, 12, 50) group2_b = np.random.normal(95, 18, 50)

fig, ax = plt.subplots()

positions_a = [1, 3] positions_b = [1.6, 3.6]

bp1 = ax.boxplot([group1_a, group2_a], positions=positions_a, widths=0.5, patch_artist=True) bp2 = ax.boxplot([group1_b, group2_b], positions=positions_b, widths=0.5, patch_artist=True)

for patch in bp1['boxes']: patch.set_facecolor('lightblue') for patch in bp2['boxes']: patch.set_facecolor('lightcoral')

ax.set_xticks([1.3, 3.3]) ax.set_xticklabels(['Group 1', 'Group 2']) ax.legend([bp1['boxes'][0], bp2['boxes'][0]], ['Method A', 'Method B'])

plt.show() ```

2. Color by Category¶

```python fig, ax = plt.subplots(figsize=(10, 5))

data_dict = { 'Control': [np.random.normal(100, 10, 50) for _ in range(3)], 'Treatment': [np.random.normal(110, 12, 50) for _ in range(3)] }

colors = {'Control': 'lightblue', 'Treatment': 'lightcoral'} positions = {'Control': [1, 4, 7], 'Treatment': [2, 5, 8]}

for label, datasets in data_dict.items(): bp = ax.boxplot(datasets, positions=positions[label], widths=0.8, patch_artist=True) for patch in bp['boxes']: patch.set_facecolor(colors[label])

ax.set_xticks([1.5, 4.5, 7.5]) ax.set_xticklabels(['Week 1', 'Week 2', 'Week 3'])

plt.show() ```

3. Legend for Groups¶

```python from matplotlib.patches import Patch

legend_elements = [Patch(facecolor='lightblue', label='Control'), Patch(facecolor='lightcoral', label='Treatment')] ax.legend(handles=legend_elements, loc='upper right') ```

Box Plot with Violin Overlay¶

Combine box plots with violin plots for complete distribution visualization.

1. Overlay Approach¶

```python import matplotlib.pyplot as plt import numpy as np

np.random.seed(42) data = [np.random.normal(0, std, 200) for std in range(1, 5)]

fig, ax = plt.subplots()

vp = ax.violinplot(data, showextrema=False) for body in vp['bodies']: body.set_alpha(0.3)

ax.boxplot(data, widths=0.1)

plt.show() ```

2. Side by Side¶

```python fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5), sharey=True)

ax1.violinplot(data) ax1.set_title('Violin Plot')

ax2.boxplot(data) ax2.set_title('Box Plot')

plt.tight_layout() plt.show() ```

3. Hybrid Visualization¶

```python fig, ax = plt.subplots()

vp = ax.violinplot(data, showmedians=False, showextrema=False) for body in vp['bodies']: body.set_facecolor('lightblue') body.set_alpha(0.5)

bp = ax.boxplot(data, widths=0.15, patch_artist=True, boxprops=dict(facecolor='white', edgecolor='black'), medianprops=dict(color='red', linewidth=2))

plt.show() ```

Exercises¶

Exercise 1. Create a figure with a box plot on the left and a histogram on the right showing the same dataset (500 samples from a skewed distribution using np.random.exponential). Use the box plot to identify the median and quartiles, then mark those same values on the histogram with vertical lines.

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
data = np.random.exponential(2, 500)

q1, median, q3 = np.percentile(data, [25, 50, 75])

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))

ax1.boxplot(data, vert=True)
ax1.set_title('Box Plot')

ax2.hist(data, bins=30, color='steelblue', edgecolor='white', alpha=0.7)
ax2.axvline(q1, color='orange', linestyle='--', label=f'Q1={q1:.2f}')
ax2.axvline(median, color='red', linestyle='-', linewidth=2, label=f'Median={median:.2f}')
ax2.axvline(q3, color='orange', linestyle='--', label=f'Q3={q3:.2f}')
ax2.legend()
ax2.set_title('Histogram with Quartile Lines')

plt.tight_layout()
plt.show()

Exercise 2. Overlay a strip plot (individual points with jitter) on top of a box plot. Generate 4 groups of 50 samples from normal distributions with different means. Show the box plot with patch_artist=True and alpha=0.5, then scatter the actual points on top.

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
data = [np.random.normal(loc=m, scale=1, size=50) for m in [2, 4, 6, 8]]

fig, ax = plt.subplots(figsize=(8, 5))
bp = ax.boxplot(data, patch_artist=True, showfliers=False)

colors = ['#a6cee3', '#b2df8a', '#fb9a99', '#fdbf6f']
for patch, color in zip(bp['boxes'], colors):
    patch.set_facecolor(color)
    patch.set_alpha(0.5)

for i, d in enumerate(data, 1):
    jitter = np.random.uniform(-0.15, 0.15, len(d))
    ax.scatter(np.full_like(d, i) + jitter, d, alpha=0.6, s=20, color='black', zorder=3)

ax.set_xticklabels(['Group 1', 'Group 2', 'Group 3', 'Group 4'])
ax.set_title('Box Plot with Strip Plot Overlay')
plt.show()

Exercise 3. Create a combined visualization with three panels stacked vertically: a box plot at the top showing distribution summary, a histogram in the middle showing frequency, and a rug plot (short vertical lines at each data point) at the bottom. Use 300 samples from a bimodal distribution (mix of two normals).

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
data = np.concatenate([np.random.normal(-2, 0.8, 150),
                        np.random.normal(2, 0.8, 150)])

fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 8),
                                      gridspec_kw={'height_ratios': [1, 3, 0.5]},
                                      sharex=True)

ax1.boxplot(data, vert=False, widths=0.6)
ax1.set_yticks([])
ax1.set_title('Distribution Summary')

ax2.hist(data, bins=40, color='steelblue', edgecolor='white')
ax2.set_ylabel('Frequency')

ax3.eventplot(data, orientation='horizontal', lineoffsets=0.5,
               linelengths=0.8, color='black', linewidths=0.5)
ax3.set_yticks([])
ax3.set_xlabel('Value')
ax3.set_ylabel('Rug')

plt.tight_layout()
plt.show()