💡 Problem Formulation: Visualizing the statistical summary of a dataset is pivotal in data analysis. A box plot is a traditional method for displaying the distribution of data based on a five-number summary: minimum, first quartile, median, third quartile, and maximum. However, by default, the mean is not shown. This article explores five methods of displaying the mean on a box plot using Python’s Matplotlib library, transforming the input data into a visual box plot enhanced with the dataset’s mean value.
Method 1: Using the ‘meanline’ Property
This method involves the use of Matplotlib’s box plot feature to enable the ‘meanline’ property. When set to “True,” this parameter allows the plotting of the mean as a line inside the box plot. It is a straightforward approach for visually representing the mean on a box plot, enhancing the ability to quickly compare the dataset’s central tendency alongside other statistical metrics.
Here’s an example:
import matplotlib.pyplot as plt import numpy as np data = np.random.randn(100) plt.boxplot(data, showmeans=True, meanline=True) plt.show()
The output is a box plot with a line representing the mean the value of the dataset.
In the above code, we first import Matplotlib’s pyplot and Numpy. We generate a random dataset of 100 points using Numpy, then use plt.boxplot(), setting showmeans to true to show the mean, and meanline to true to display the mean as a line.
Method 2: Adding a ‘mean’ Annotation
This technique involves computing the mean of the dataset and using Pyplot’s annotation functionality to add the mean value as text within the plot. This method does not only add a visual cue to the mean value but also provides the exact numerical mean value on the box plot, which can be particularly useful for reports or presentations.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
data = np.random.randn(100)
mean_value = np.mean(data)
plt.boxplot(data, showmeans=True)
plt.annotate(f'Mean: {mean_value:.2f}', xy=(1, mean_value), xytext=(1.1, mean_value),
arrowprops=dict(facecolor='black', shrink=0.05))
plt.show()The output is a box plot with an annotated arrow pointing to the mean value.
Here we calculate the mean using Numpy’s np.mean() on our dataset. We then draw a box plot with plt.boxplot(). Lastly, we use plt.annotate() to create textual annotation on the plot for the mean value, with an arrow pointing to where the mean lies on the box plot for clearer indication.
Method 3: Using a Custom Scatter Plot
Another way to show the mean on a box plot is by plotting a custom scatter plot on top of the box plot. This involves overlaying a scatter plot point that specifically marks the mean value. This method is highly customizable in terms of point aesthetics and it can be useful for distinguishing the mean clearly from other elements of the box plot.
Here’s an example:
import matplotlib.pyplot as plt import numpy as np data = np.random.randn(100) mean_value = np.mean(data) plt.boxplot(data) plt.scatter(1, mean_value, color='red', zorder=3) # zorder ensures the point is above the box plot plt.show()
The output is a box plot with a prominent red dot denoting the mean.
After plotting the box plot using plt.boxplot(), we simply add a scatter plot with plt.scatter(), setting the coordinates to (1, mean_value) so that the red dot appears right at the average of our dataset, above all other elements due to the zorder property.
Method 4: Customizing Whisker Caps
Matplotlib allows customization of different elements of a box plot, including the caps on the whiskers. By customizing the whisker caps, one can modify the appearance of the caps that could encapsulate the mean indicator. While not a direct means of showing the mean, altering whisker appearances can offer a subtle visual clue that can be associated with the mean if explained adequately in the plot legend or a caption.
Here’s an example:
import matplotlib.pyplot as plt import numpy as np data = np.random.randn(100) mean_value = np.mean(data) plt.boxplot(data, meanprops=dict(marker='D', markeredgecolor='black', markerfacecolor='black')) plt.show()
The output is a box plot with diamond-shaped markers on the whiskers associated with the mean value.
First, we draw a standard box plot with plt.boxplot(). Through the meanprops dictionary, we pass custom properties for the mean marker; specifically, we choose a ‘D’ (diamond) marker with a black color that we associate with the mean of our data, making it stand out.
Bonus One-Liner Method 5: Mean as a Horizontal Line
An elegantly simple method to show the mean is by drawing a horizontal line across the entire figure at the height of the mean value. This one-liner solution emphasizes the mean across the entire plot, making it immediately apparent where the mean lies in relation to the rest of the data.
Here’s an example:
import matplotlib.pyplot as plt import numpy as np data = np.random.randn(100) mean_value = np.mean(data) plt.boxplot(data) plt.axhline(y=mean_value, color='g', linestyle='--') plt.show()
The output is a box plot intersected by a dashed green horizontal line at the mean value.
Below the box plot, created using plt.boxplot(), we simply draw a horizontal line with plt.axhline(). This horizontal line is set to the mean value and is styled with a green color and a dashed pattern for clear visibility against the box plot.
Summary/Discussion
- Method 1: Using ‘meanline’. Strengths: Simple, direct visualization of mean. Weaknesses: Less customizable.
- Method 2: Adding ‘mean’ Annotation. Strengths: Provides exact numerical value. Weaknesses: Potentially cluttered if plot is small or has many outliers.
- Method 3: Using a Custom Scatter Plot. Strengths: Highly customizable visual cue. Weaknesses: Can be obscured by other plot elements if not careful with z-ordering.
- Method 4: Customizing Whisker Caps. Strengths: Subtle, legend-driven indicator. Weaknesses: Indirect method, requires explanation.
- Bonus Method 5: Mean as a Horizontal Line. Strengths: Clear, spans entire plot width. Weaknesses: Not box-centric, might be confused with other summary statistics.