Pizza is one of my favorite foods. Recently, I was at a restaurant trying to determine how many pizzas and sizes I needed. The restaurant displayed a few meshes, similar to the ones from the image below, to provide a guide for the size of their pizzas.
My dilemma was determining if it made more sense to get two small size pizzas (8" for $9.49 each) or a medium one (12" for $16.99). I could have easily calculated the area of the circles (A = pi*rˆ2) to figure this out. However, I decided to estimate which of the options would be the best for me. Afterwards, this led me to ask if I had made the right decision? I had not!
To determine if this was a common mistake, I turned to my coworkers and social media to run an informal survey to understand what choices people would make. I asked them to select which area they thought was bigger, the big circle or the two small ones. What would you have chosen?
From the 30 respondents to my survey, there was an almost equal divide between the number of people who selected each option. Specifically, 14 people (47%) chose the big circle compared to 16 people (53%) who selected the two small circles. So what is the right answer? The big and small circles are drawn to scale to represent a pizza with a 12 and 8 inch diameter, respectively. As a result the medium pizza has an area of 113 inchesˆ2 compared to the two small pizzas that have an area of 100 inchesˆ2. Not only is the big circle about 13% larger than the two small ones, it also ends up being significantly less expensive!!! The medium pizza cost $16.99 ($0.15 / inchˆ2) compared to $18.98 ($0.19 / inchˆ2) for the two small ones.
So, how does this apply to data visualization? One of the popular tools we use during data visualization is comparing areas of different objects. We notice this in several chart types such as bubble charts and bubble scatter plots.
The image below is an example of a bubble chart that displays the number of universities per country. The United States clearly displays the highest number, but how many less universities does India have? Or if we added India and Japan, would we have more universities than the United States? These questions cannot be properly answered just by looking at the chart.
Example of a Bubble Chart which displays the number of universities per country
From the image above, it is clear that we would have a difficult time understanding what the difference is between the different circle sizes. The most we would be able to do, is determine if a circle is bigger than another, but we would have a hard time quantifying how much bigger.
This challenge is not only limited to circles but to any two dimensional geometric shape. Below we present an example of a tree map. Which is bigger, the Romance Books or Rock Music?
Example of a Treemap
Another example would be the pie chart below. Which slice is bigger the orange or green? And how much bigger is it?
Example of a Pie Chart
The reality is that we have a hard time at estimating areas (or volumes for that matter), which has made these types of visualizations ineffective for obtaining quantitative information. Below we present a few different shapes, which do you think has the biggest area?
Different shapes that have the same area
All the images above have the same area!
In summary, we are ill equipped when comparing areas of shapes. We should be careful when selecting charts that compare areas for our visualizations. A better chart type could be one that compares lengths of objects instead of areas, such as bar charts.