There is only one place for most 3D graphs, and that is the trash bin! The large majority of 3D graphs used in general or business context are confusing to interpret and prone to be misread. Popular data visualisation tools such as ggplot for R and Tableau do not even have the provision for 3D graphs, since most data visualisation experts discourage their usage.

Tableau and ggplot are based on the grammar of graphics, a layered framework to concisely describe the components of any type of graph. The grammar of graphics gained popularity via ggplot and over time became the substrate for other visual analysis tools such as plotline for Python, D3, and Tableau. It has over time become a robust standard for visualising data and composing well-designed graphs based not on their names but on statistics and primary visual elements – and it does not allow 3D graphs.

### Why are 3D constructs so frowned upon by most data visualisation experts? Representing quantities with 3D objects poses multiple problems. Edward Tufte in his book *The Visual **Display of Quantitative Informatio*n illustrates this with a graph which uses barrels of oil to represent the price of crude oil over time.

Look at the above figure, which contains two barrels. Can you estimate the amount represented by the bigger barrel if the smaller barrel represents ten units of the currency? Do write down your answer before reading further.

What did you compare – heights, surface areas or volumes of the two barrels? If heights are compared, then the bigger barrel represents 20 units, and if we compare the surface areas, it represents around 30 units. If, however, the volumes are compared, the bigger barrel is more than five times the size of the smaller barrel and hence represents around 50 units, more than double what the height represents! How close did you get? Most viewers tend to compare volumes, which are, however, difficult to estimate accurately.

The conundrum in Tufte’s example is similar – while the prices were represented by the height of the barrels, the graph was misleading because most viewers compared the volumes of the barrels.

William Cleveland and Robert McGill, in their landmark paper on graphical perception, establish through a series of experiments that visually judging differences in quantities is easiest when the quantities are represented in one dimension (eg, as heights of bars) instead of areas of shapes or volumes of objects. As we discussed in the earlier chapter, representing quantities as 2D shapes, for example, as areas of circles, makes it much trickier to estimate differences in quantities. This problem gets further heightened when we need to estimate quantities represented as 3D objects, for example, as volumes of spheres.

Try this quick exercise out for yourself. In the above figure, we have pairs of bars, circles, and spheres. Can you estimate the ratio of the heights of the two bars? Now estimate the ratio of the areas of the two circles. Now move on to the spheres. If you guessed that the smaller bar is around three quarters of the bigger bar, you are absolutely right! What were your estimates for the circles and spheres? Are you surprised to know that their ratios are also 4:3?

### The volume of the smaller sphere is indeed three-quarters the volume of the bigger sphere. You might have realised through this exercise that it is certainly very difficult for our brain to estimate differences in volume. In the study mentioned earlier, Cleveland and McGill establish that viewers tend to underestimate areas and volumes. In fact, they also show that the underestimation in volumes (3D objects) is more acute than in areas (2D shapes).

Given how human perception and cognition work, it seems prudent to refrain from using 3D objects to represent values, especially when there are more dependable alternatives available, like the length of a bar or the height of a dot. There are primarily two scenarios where 3D constructs are used in business charts. The first scenario pertains to situations where there are three variables which need to be presented.

As an example, consider a company which wants to compare monthly sales for three different product categories in four different regions, via three different channels. With one axis for the quantitative value (sales in this case), the remaining two axes could be used for two of the three variables, say region and channel. The third variable could be accommodated by using pairs of clustered bars (we will come back to this scenario in a bit).

The second scenario where 3D graphs are used, typically involves only one variable which needs to be visualised. Nevertheless, a 3D object or space is used in such situations primarily to add some “visual appeal” (for lack of a better way to articulate the reason!) to the graph. The oil barrel example discussed earlier falls under this category. Rest assured that for both these scenarios, there are more effective ways to depict the data than to resort to 3D constructs, as we shall shortly see. We will first tackle the second scenario where 3D objects are employed to make the graph visually appealing and then go on to the first scenario of visualising multiple variables.

*Excerpted with permission from *Impactful Data Visualization: Hide and Seek with Graphs, *Kavitha Ranganathan, Penguin.*

*We welcome your comments at letters@scroll.in.*