# Bubble chart

This bubble chart show the relationship between three variables.
A series of bubbles on a map is called a cartogram or sometimes "bubble map".

A bubble chart is a type of chart that displays three dimensions of data. Each entity with its triplet (v1, v2, v3) of associated data is plotted as a disk that expresses two of the vi values through the disk's xy location and the third through its size. Bubble charts can facilitate the understanding of social, economical, medical, and other scientific relationships.

Bubble charts can be considered a variation of the scatter plot, in which the data points are replaced with bubbles. As the documentation for Microsoft Office explains, "You can use a bubble chart instead of a scatter chart if your data has three data series that each contain a set of values. The sizes of the bubbles are determined by the values in the third data series.".[1]

## Choosing bubble sizes correctly

The human visual system naturally experiences a disk's size in terms of its area. And the area of a disk—unlike its diameter or circumference—is not proportional to its radius, but to the square of the radius. So if one chooses to scale the disks' radii to the third data values directly, then the apparent size differences among the disks will be non-linear (quadratic) and misleading. To get a properly weighted scale, one must scale each disk's radius to the square root of the corresponding data value v3. This scaling issue can lead to extreme misinterpretations, especially where the range of the data has a large spread. And because many people are unfamiliar with—or do not stop to consider—the issue and its impact on perception, those who are aware of it often have to hesitate in interpreting a bubble chart because they cannot assume that the scaling correction was indeed made. So it is important that bubble charts not only be scaled in this way, but also be clearly labeled to document that it is area, rather than radius or diameter, that conveys the data.[2]

## Displaying zero or negative data values in bubble charts

The metaphoric representation of data values as disk areas cannot be extended for displaying values that are negative or zero. As a fallback, some users of bubble charts resort to graphic symbology to express nonpositive data values. As an example, a negative value ${\displaystyle v<0}$ can be represented by a disk of area ${\displaystyle v}$ in which is centered some chosen symbol like "×" to indicate that the size of the bubble represents the absolute value of a negative data value. And this approach can be reasonably effective in situations where data values' magnitudes (absolute values) are themselves somewhat important—in other words, where values of ${\displaystyle v}$ and ${\displaystyle -v}$ are similar in some context-specific way—so that their being represented by congruent disks makes sense.

To represent zero-valued data, some users dispense with disks altogether, using, say, a square centered at the appropriate location. Others use full circles for positive, and empty circles for negative values.

## Incorporating further dimensions of data

The value can be proportional to the diameter or the area of the bubble. The example of the Portfolio Management Simulation SimulTrain uses different areas and colors of the bubbles.

Additional information about the entities beyond their three primary values can often be incorporated by rendering their disks in colors and patterns that are chosen in a systematic way. And, of course, supplemental information can be added by annotating disks with textual information, sometimes as simple as unique identifying labels for cross-referencing to explanatory keys and the like.