Box Plot

Author: Dr. Hannah Volk-Jesussek
Updated: October 20, 2025

What is a boxplot? With a box plot you can graphically display a lot of information about your data. Among other things, the median, the interquartile range (IQR) and the outliers can be read off from a box plot.

The data used are mostly metric scaled, such as a person's age, annual electricity consumption, or temperature. Often a box plot is created to compare and contrast two or more groups. For example, the age of different groups.

How is a box plot interpreted?

The box itself indicates the range in which the middle 50% of all values lie. Thus, the lower end of the box is the 1st quartile and the upper end is the 3rd quartile.

Therefore, 25% of the data lie below Q1, 25% above Q3, and 50% within the box.

Let's say we look at the age of individuals in a box plot, and Q1 is 31 years, then it means that 25% of the participants are younger than 31 years. If Q3 is 63 years, then it means that 25% of the participants are older than 63 years, 50% of the participants are therefore between 31 and 63 years old. Thus, between Q1 and Q3 is the interquartile range.

In the box plot, the solid line indicates the median and the dashed line indicates the mean.

For example, if the median is 42, this means that half of the participants are younger than 42 and the other half are older than 42. The median thus divides the individuals into two equal groups.

The T-shaped whiskers go to the last point, which is still within 1.5 times the interquartile range. What does it mean? The T-shaped whisker is either the maximum value of your data but at most 1.5 times the interquartile range. Any observations that are more than 1.5 interquartile range (IQR) below Q1 or more than 1.5 IQR above Q3 are considered outliers. If there are no outliers, the whisker is the maximum value.

So the upper whisker is either the maximum value or 1.5 times the interquartile range. Depending on which value is smaller. The same is true for the lower whisker, which is either the minimum or 1.5 times the interquartile range.

Points that are further away (beyond the fences are considered outliers. If no point is further away than 1.5 times the interquartile range, the T-shaped whisker indicates the maximum or minimum value.

Box plot Example

Studying Patient Recovery Times for Different Treatments

In a medical study, researchers may be examining recovery times for patients undergoing different types of treatment for the same condition.

By using box plots for each treatment type, researchers can visualize the distribution of recovery times. They can see the median recovery time for each treatment, the range of times, and any outliers (e.g., unusually long or short recovery times).

This helps in determining which treatment may be most effective, or whether some treatments have more variable outcomes than others.

Create box plot online

With numiqo you can easily create a box plot online. To do this, click on the statistics calculator, copy your own data into the table, select the tab "Descriptive" or "Charts" and click on the variables for which you want to create a box plot.

In the upper box plot created with numiqo online, each box represents age for one location of fall (aisle, bathroom, recreation room and hospital).