Use Box Plots with Caution! They Can Be Misleading.

...and here's how to prevent being misled by them.

Avi Chawla

Feb 16, 2024

Box plots are pretty common in data analysis.

Yet, they can be highly misleading at times.

Let’s understand how!

To begin, a box plot is a graphical representation of just five numbers:

min
first quartile
median
third quartile
max

This means that if two entirely different distributions have similar five values, they will produce identical box plots.

This is evident from the image below:

As depicted above, three datasets have the same box plots, but entirely different distributions.

This shows that solely looking at a bar plot may lead to incorrect or misleading conclusions.

Here, the takeaway is not that box plots should not be used.

Instead, it’s similar to what we saw in one of the earlier posts about correlation: “Whenever we generate any summary statistic, we lose essential information.”

Correlation is also a summary statistic, and as shown below, adding just two outliers changes the direction of correlation:

**Why Correlation (and Other Summary Statistics) Can Be Misleading**

Thus, it is always important to look at the underlying data distribution.

For instance, whenever I create a box plot, I create a violin (or KDE) plot too. This lets me validate whether summary statistics resonate with the data distribution.

In fact, I also find Raincloud plots to be pretty useful.

They provide a pretty concise way to combine and visualize three different types of plots together.

These include:

Box plots for data statistics.
Strip plots for data overview.
KDE plots for the probability distribution of data.

👉 Over to you: What other measures do you take when using summary statistics?

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