Basic Box Plot¶

Box plots (box-and-whisker plots) visualize the distribution of data through quartiles, providing a compact summary of central tendency, spread, and outliers.

Single Data Set¶

The simplest box plot displays one distribution using ax.boxplot().

1. Import and Setup¶

python import matplotlib.pyplot as plt import numpy as np

2. Generate Data¶

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

3. Create Box Plot¶

python fig, ax = plt.subplots() ax.boxplot(data) ax.set_ylabel('Value') ax.set_title('Basic Box Plot') plt.show()

Multiple Data Sets¶

Compare multiple distributions side by side by passing a list of arrays.

1. Prepare Multiple Arrays¶

python np.random.seed(42) data1 = np.random.normal(100, 10, 200) data2 = np.random.normal(90, 20, 200) data3 = np.random.normal(110, 15, 200)

2. Pass as List¶

python fig, ax = plt.subplots() ax.boxplot([data1, data2, data3]) ax.set_xticklabels(['Group A', 'Group B', 'Group C']) ax.set_ylabel('Value') ax.set_title('Comparing Distributions') plt.show()

3. Interpret Results¶

Each box represents one distribution. Boxes at different heights indicate different medians. Wider boxes (taller IQR) indicate greater variability.

Method Signature¶

The ax.boxplot() method accepts various input formats.

1. Single Array¶

python ax.boxplot(data) # One box

2. List of Arrays¶

python ax.boxplot([data1, data2, data3]) # Multiple boxes

3. 2D Array¶

python data_2d = np.random.randn(100, 4) ax.boxplot(data_2d) # Each column becomes a box

Exercises¶

Exercise 1. Generate three datasets from different distributions: normal (mean=0, std=1), uniform (low=-2, high=2), and exponential (scale=1) with 200 samples each. Create side-by-side box plots for all three and label each with the distribution name.

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
normal_data = np.random.normal(0, 1, 200)
uniform_data = np.random.uniform(-2, 2, 200)
exponential_data = np.random.exponential(1, 200)

fig, ax = plt.subplots(figsize=(8, 5))
ax.boxplot([normal_data, uniform_data, exponential_data],
            labels=['Normal(0,1)', 'Uniform(-2,2)', 'Exponential(1)'])
ax.set_ylabel('Value')
ax.set_title('Distribution Comparison')
plt.show()

Exercise 2. Create a horizontal box plot of test scores for four classes. Generate data with np.random.normal using means [70, 75, 80, 85] and standard deviation 10 for each class (100 students each). Add class labels and a vertical line at the overall mean.

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
means = [70, 75, 80, 85]
data = [np.random.normal(m, 10, 100) for m in means]
overall_mean = np.mean([d.mean() for d in data])

fig, ax = plt.subplots(figsize=(8, 5))
ax.boxplot(data, vert=False, labels=['Class A', 'Class B', 'Class C', 'Class D'])
ax.axvline(x=overall_mean, color='red', linestyle='--', label=f'Overall Mean = {overall_mean:.1f}')
ax.set_xlabel('Test Score')
ax.set_title('Test Scores by Class')
ax.legend()
plt.show()

Exercise 3. Create a box plot comparing the distributions of sin(x), cos(x), and tan(x) evaluated at 1000 random points uniformly distributed in \([0, 2\pi]\). Clip the tan(x) values to \([-10, 10]\). Show notched box plots to indicate confidence intervals around the median.

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
x = np.random.uniform(0, 2 * np.pi, 1000)
sin_vals = np.sin(x)
cos_vals = np.cos(x)
tan_vals = np.clip(np.tan(x), -10, 10)

fig, ax = plt.subplots(figsize=(8, 5))
ax.boxplot([sin_vals, cos_vals, tan_vals],
            labels=['sin(x)', 'cos(x)', 'tan(x)'],
            notch=True)
ax.set_ylabel('Value')
ax.set_title('Trig Function Distributions (Notched)')
plt.show()