# The Whole Story on Part to Whole Relationships

Part to whole relationships are an important component in several different visualization types. They are a simple relationship in the data; mathematically, this relationship is equivalent to percentages. Obviously, this means if the data is percentages, the part to whole relationship exists, but even data that isn’t represented as a percentage can have a part to whole relationship. Some examples would include a budget breakdown by dollars, a comparison of square miles for each state in the US, or the volume ratios in your favorite pie recipe. Pie charts are the most obvious visualization that have a part to whole relationship. Each slice represents a part of the whole pie. This delicious metaphor is easy to understand and has helped to drive the pie chart’s popularity. Unfortunately, visually representing data with a part to whole relationship can remove quantitative information. Percentages do not tell anything about the total, they only tell about the relationship between the parts. This same downside is true of many visual part to whole representations. In the two charts below, it is impossible to visually tell quantities, while it is simple to see the ratios within each group. While the labels do let us know the totals, reading is very different from seeing. The pie charts below show how many crew members of the Titanic survived (and did not survive), by gender. One method to allow for the visual comparison of the totals is to re-size each pie chart based on the total. (It is important to do the math so that you do not scale quadratically!) This particular data set has a hierarchy of part to whole relationships, and that lets us do some cool stuff with other visualization types. Treemaps show both a hierarchy, and have part to whole relationships. For this small branch of the hierarchy, a treemap’s advantages don’t really show, but if we visualize the full hierarchy as well we get a pretty clear picture. By using the part to whole relationship on each level of the hierarchy, we can compare quantities between any two parts as well as between parts and groups. For example, we can see that the number of male crew members that did not survive is greater than the entire first class. This type of comparison can happen entirely through visualization, without the viewer using the numbers on the labels or doing any math. In addition to pie charts and treemaps, there are a few other common visualizations that display part to whole relationships.

Visualizing part to whole relationships can offer several advantages, but you should also be aware of the ratio and quantity comparison issues that they can create. To download the titanic data used in this post, click here.

Drew Skau is a PhD Computer Science Visualization student at UNCC, with an undergraduate degree in Architecture.