Box Plots for Categorical Variables (boxplot)

While bar plots give us a sense of the central tendency (like the mean or median) for a numerical variable across different categories, they don't tell us much about how the data is spread out within each category. Are the values tightly clustered, or widely dispersed? Are there many outliers? To answer these questions and compare the overall distributions, we can use box plots.

A box plot (or box-and-whisker plot) provides a concise visual summary of a dataset's distribution. It displays five key statistics:

1. Median (Q2): The middle value of the data (50th percentile), represented by a line inside the box.
2. First Quartile (Q1): The value below which 25% of the data falls (25th percentile). This is the bottom edge of the box.
3. Third Quartile (Q3): The value below which 75% of the data falls (75th percentile). This is the top edge of the box.
4. Interquartile Range (IQR): The range between Q1 and Q3 (IQR = Q3 - Q1). The box itself represents the IQR, containing the middle 50% of the data.
5. Whiskers: Lines extending from the box, typically showing the range of the data within 1.5 times the IQR from Q1 and Q3. Points outside the whiskers are often considered potential outliers and plotted individually.

Seaborn's boxplot function is specifically designed to create these visualizations, making it easy to compare distributions across different categories.

Creating Box Plots with seaborn.boxplot

The basic syntax involves specifying the categorical variable for one axis (usually x), the numerical variable for the other axis (usually y), and the DataFrame containing the data using the data parameter.

Let's use the familiar 'tips' dataset that comes with Seaborn. We can compare the distribution of total bill amounts for each day of the week.

import seaborn as sns
import matplotlib.pyplot as plt
import pandas as pd

# Load the example dataset
tips = sns.load_dataset("tips")

# Create the box plot
plt.figure(figsize=(8, 5)) # Adjust figure size for better readability
sns.boxplot(x="day", y="total_bill", data=tips, palette=["#74c0fc", "#ffc078", "#8ce99a", "#ffc9c9"])

# Add title and labels (optional but recommended)
plt.title("Distribution of Total Bill Amounts by Day")
plt.xlabel("Day of the Week")
plt.ylabel("Total Bill ($)")

# Show the plot
plt.show()

Distribution of total bill amounts across different days of the week using Seaborn's boxplot.

Interpreting the Box Plot

From the plot above, we can draw several observations:

• Median: The line inside each box shows the median total bill. Saturdays and Sundays tend to have higher median bills than Thursdays and Fridays.
• Spread (IQR): The height of the box (IQR) indicates the spread of the middle 50% of bills. Saturdays seem to have a larger IQR, suggesting more variability in bill amounts compared to Thursdays.
• Whiskers: The whiskers show the range of typical bills. Weekend days (Saturday, Sunday) appear to have a wider range, extending to higher values.
• Outliers: Individual points plotted beyond the whiskers represent potential outliers. Sundays and Saturdays show several high-value outliers, indicating some exceptionally large bills on those days. Thursday also has one quite high outlier.

Compared to a bar plot showing only the average bill per day, the box plot gives us a much richer understanding of how bill amounts vary within each day.

Customizing Box Plots

Like other Seaborn functions, boxplot offers various customization options.

• Orientation: You can create horizontal box plots by swapping x and y or setting orient='h'.

  # Horizontal box plot
  sns.boxplot(x="total_bill", y="day", data=tips, orient='h', palette=["#74c0fc", "#ffc078", "#8ce99a", "#ffc9c9"])
  plt.title("Distribution of Total Bill Amounts by Day")
  plt.xlabel("Total Bill ($)")
  plt.ylabel("Day of the Week")
  plt.show()
  

• Order: Control the order in which categories appear using the order parameter, passing a list of category names.

  # Specify order of days
  day_order = ["Thur", "Fri", "Sat", "Sun"]
  sns.boxplot(x="day", y="total_bill", data=tips, order=day_order, palette=["#74c0fc", "#ffc078", "#8ce99a", "#ffc9c9"])
  # ... (add titles/labels and show plot)
  

• Hue: You can add another categorical dimension using the hue parameter, which creates separate, side-by-side boxes for each level of the hue variable within each main category on the x-axis. For example, you could compare bills by day, split by whether the customer was a smoker.

  # Add 'smoker' as a hue dimension
  sns.boxplot(x="day", y="total_bill", hue="smoker", data=tips, palette="pastel")
  plt.title("Distribution of Total Bill by Day and Smoker Status")
  plt.xlabel("Day of the Week")
  plt.ylabel("Total Bill ($)")
  plt.show()
  

Box plots are particularly effective when you want to compare the distributions of a numerical variable across several groups defined by one or more categorical variables. They provide a quick way to assess differences in central tendency, spread, and the presence of outliers between the groups.