Through the visual representation of a dataset, boxplots are very informative and very useful when comparing distributions between two or more processes.

**What Are Boxplots**

Through the visual representation of a dataset, boxplots are very informative and very useful when comparing distributions between two or more processes. Essentially, boxplots summarize the following statistics:

- The lower whisker contains 25% of the data (first quartile, or Q1)
- The box itself contains 50% of the data (inter-quartile range)
- The upper whisker contains 25% of the data and up to it, 75% of the data (third quartile, or Q3)
- The line right in the middle of the box is normally the median, Q2 (although some statistical software may also display the mean)
- Outliers are far away data points that are usually 1.5 greater in value than the length of the box itself (the inter-quartile range)

The Five-Number Summary

The Five-Number Summary is what is displayed graphically in a boxplot. The five numbers are:

- The minimum value (Q0)
- The first quartile (Q1)
- The median (or second quartile, Q2)
- The third quartile (Q3)
- The maximum value (Q4)

Practical Example

A call centre manager wishes to know how long it is taking for three distinct branches (A, B, and C) to respond to client calls. The following comparative boxplots suggest that: 1) branch A has the greatest amount of variation (size of the box and extent of whiskers) however a lower median response time, 2) branches B and C have less variation however slower median response times, and 3) branches B and C showcase outliers in their processes; branch C in this case on both ends of the upper and lower whiskers.

**Boxplot Limitations (Words of Caution)**

Boxplots do not always display the number of data points being graphed. For example, one might be looking at two comparative boxplots, the first one with only 5 distinct numbers (the Five-Number Summary that is displayed in a boxplot), and another one with 500 data points, making it a stronger representation of that process’s central tendency and spread. So, use caution when interpreting boxplots!

**The Boxplotly Playground**

Check out this web app built by the author of this post to learn more about and interactively play with Boxplots online.

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