Box Plot Anatomy¶

Understanding the visual components of a box plot is essential for proper interpretation of distributional data.

Visual Components¶

A box plot consists of five primary visual elements that summarize the distribution.

1. The Box¶

The rectangular box spans from the first quartile (Q1, 25th percentile) to the third quartile (Q3, 75th percentile). This range is called the Interquartile Range (IQR).

IQR = Q3 - Q1

2. The Median Line¶

The horizontal line inside the box represents the median (Q2, 50th percentile). Its position within the box indicates skewness.

3. The Whiskers¶

Vertical lines extend from the box to show the range of non-outlier data. By default, whiskers extend to 1.5 × IQR from the box edges.

lower_whisker = Q1 - 1.5 * IQR
upper_whisker = Q3 + 1.5 * IQR

4. The Fliers (Outliers)¶

Points beyond the whiskers are plotted individually as outliers (fliers). These represent extreme values in the distribution.

5. The Caps¶

Short horizontal lines at whisker ends mark the extent of non-outlier data.

Statistical Interpretation¶

The box plot encodes the five-number summary plus outlier detection.

1. Five-Number Summary¶

import numpy as np

data = np.random.normal(100, 15, 200)

minimum = np.min(data)
q1 = np.percentile(data, 25)
median = np.percentile(data, 50)
q3 = np.percentile(data, 75)
maximum = np.max(data)

2. Spread Indicators¶

The box width (IQR) shows the middle 50% of data. Tall boxes indicate high variability; short boxes indicate consistency.

3. Skewness Detection¶

When the median line is not centered in the box, the distribution is skewed. Median closer to Q1 indicates right skew; closer to Q3 indicates left skew.

Comparison with Histogram¶

Box plots and histograms both show distributions but emphasize different aspects.

1. Box Plot Strengths¶

Box plots excel at comparing multiple distributions side-by-side, identifying outliers, and showing quartile information compactly.

2. Histogram Strengths¶

Histograms reveal the shape of the distribution, multimodality, and density patterns that box plots cannot show.

3. Combined View¶

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
data = np.random.normal(100, 15, 200)

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

ax1.hist(data, bins=20, edgecolor='black', alpha=0.7)
ax1.set_title('Histogram')

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

plt.tight_layout()
plt.show()