Image by Editor | Midjourney

Violin plots and box plots are basic visualization tools in data analysis and statistics. Both showcase distributions in different ways and, therefore are used for different purposes.

Choosing which one to use in a given scenario requires a good understanding of the differences between them and to have a clear objective in mind.

This article aims to break down their key features and advantages, making it easier for you to decide when to use one or the other.

Let’s get started!

What is a Box Plot?

A box plot (known as a box-and-whisker plot) is a statistical chart for visualizing the distribution, variability, and skewness of numerical data.

An example of a box plot | Image by Author

It provides a concise summary of the dataset through:

• Minimum: The smallest value in the data (outliers aside)
• First Quartile (Q1): The 25th percentile, represented by the bottom of the box
• Median (Q2): The 50th percentile or the middle, the line inside the box
• Third Quartile (Q3): The 75th percentile, represented by the top of the box
• Maximum: The largest value in the data (outliers aside)

The box spans from Q1 to Q3, representing the interquartile range. Furthermore, whiskers extend from the box to indicate the range of the data within 1.5 times the IQR, displaying outliers outside the range.

Boxplots provide a straightforward way to assess a dataset’s central tendency, spread, and asymmetry, making them a go-to tool for exploratory data analysis.

What is a Violin Plot?

A violin plot is a versatile chart that displays summary statistics such as the median, quartiles, and range. As opposed to box plots, it goes a step further by including an illustration of the density of the data across different values, offering deeper insights into its distribution.

Example of a violin plot | Image by Author

It combines the structure of a box plot with a mirrored kernel density plot. This dual representation highlights the central tendency and variability and reveals the probability density too, showing how data is distributed at various levels. The unique shape of a violin plot can capture nuances such as multiple modes in the data, which a box plot may overlook.

This makes violin plots particularly valuable when you need a more detailed view of the data’s variability and distribution, including patterns like clustering or multimodality. They are ideal for comparing distributions across categories while providing a comprehensive visual summary.

Key Differences Between Box Plots and Violin Plots

Shape and Representation of Distribution

• Box Plot: Displays a simple rectangular box with whiskers extending outward. It focuses on quartiles, ranges, and outliers, offering a clear, concise view of the central tendency and variability. This simplicity makes it ideal for quick comparisons.
• Violin Plot: Features a more intricate shape resembling a violin, with its width at any given point corresponding to the data density at that value. This allows for a richer visualization of the distribution, capturing patterns like multiple peaks or subtle nuances in the data.

Display of Density

• Box Plot: It presents only the minimum, maximum, median, and quartiles, which limits insights into how data points are distributed between these summary statistics.
• Violin Plot: Includes a full kernel density estimation, offering a visual representation of where data points are concentrated. This makes it particularly useful for identifying whether the data is unimodal, multimodal, or exhibits skewness.

Symmetry and Outliers

• Box Plot: Highlights symmetry or skewness using the box and whiskers, and specifically marks outliers as individual points, making it easy to identify extreme values and assess distribution balance.
• Violin Plot: Also reflects symmetry but provides a more detailed view of the distribution shape. While outliers aren’t explicitly marked, density peaks can often indicate areas where extreme values are likely to occur.

Use a Box Plot When…

• You need a quick summary of the data distribution.
• Your focus is on comparing medians, ranges, and identifying outliers.
• Simplicity and ease of interpretation are a priority.
• Your dataset is unimodal and has little to no skewness.

Use a Violin Plot When…

• You require detailed insights into the data distribution, including density variations.
• You’re working with multimodal distributions or want to visualize subtle patterns in the data.
• You want to compare multiple distributions while also observing their shape and spread.
• Your focus is on the overall distribution form, rather than identifying individual outliers.

Wrapping Up

Both plots have their strengths: box plots excel in simplicity and clarity, while violin plots provide a richer, more nuanced view of the data. Choose the one that best fits your analysis goals.