2.2.1. Circle diagram (a.k.a. Pie chart)

As the name implies a circle diagram is a circle divided into slices, each representing a category as in the example shown in Figure 3. 

Figure 3. Example of a pie chart

A circle has 360 degrees, equal to 100%. So by multiplying the relative frequencies with 360, the degrees for each category can be found. This means that visually the circle diagram can only show the relative frequencies.

The circle diagram is quite popular and often used, but actually has a few disadvantages:

• It can only show relative frequencies. To show other frequencies the numbers themselves have to be added.
• When the relative frequencies are close to each other, the differences are not easily seen in a circle diagram.
• When there are many categories the circle diagram will look very busy and not easily to read. 
• The circle diagram can only show one variable.
• Do not use a pie chart for results of a multiple answer questions

An example of a 'bad' circle diagram was created by a program called ‘The Archivist’ and used in an article online (Perez, 2009) is shown in Figure 4.


Figure 4. Example of a pie chart with too many slices. Reprinted from 10 Ways to Archive Your Tweets, by S. Perez, 2009, Retrieved from http://readwrite.com/2009/08/10/10_ways_to_archive_your_tweets.

There are clearly too many categories and the few biggest slices are difficult to tell which is bigger. A possible solution in this case could have been to group the smallest categories into one category 'Other' and then still use a bar-chart instead.

Another example of a 'bad' circle diagram comes from The Economist (as cited in Kyd, 2012) shown in Figure 5.


Figure 5. Example of pie chart with rel. freq. too close to each other. Reprinted from Good Examples of Bad Charts: Chart Junk from a Surprising Source, by C. Kyd, 2012, Retrieved from http://exceluser.com/blog/1133/good-examples-of-bad-charts-chart-junk-from-a-surprising-source.html


It is very difficult to see the differences. It is not until you look at the numbers that you can tell which slices are bigger or smaller (with a few exceptions). A bar-chart would have been preferred.

A third example comes from fox-news, shown in Figure 6.


Figure 6. Example of a pie chart with percentages not adding up to 100.

This seems pretty odd that the percentages do not add up to 100%. This is probably because people could choose multiple options. The size of the slices is then most somewhat irrelevant. A bar-chart would have been preferred here.

There are many variations to the circle diagram. Some only add a visual effect (moving one or more slices out of the center a.k.a. exploded, or creating a 3D effect), and some more complex variations (such as the polar charts made famous by Florence Nightingale, doughnut charts, spie charts, etc.).

History
The earliest found circle diagram is found on the inlay of a book by William Playfair (1801) shown in Figure 7:


Figure 7. Earliest found pie chart. Reprinted from The statistical breviary: shewing the resources of every state and kingdom (p. inlay), by W. Playfair, 1801, London: T. Bensley

The name 'pie chart' might come from a misspelling of the word Pi. Pi is often associated with a circle. It might also simply come from the resemblances with a pie (as in apple-pie). However Srivastava & Rego (2011) put forward another belief that it is named after a royal French cook Pie, who served dishes in a pie-chart shape.

>>Next section: Bar-chart

References
Kyd, C. (2012, April 5). Good Examples of Bad Charts: Chart Junk from a Surprising Source. ExcelUser. Retrieved from http://exceluser.com/blog/1133/good-examples-of-bad-charts-chart-junk-from-a-surprising-source.html
Perez, S. (2009, August 10). 10 Ways to Archive Your Tweets. ReadWrite. Retrieved April 27, 2014, from http://readwrite.com/2009/08/10/10_ways_to_archive_your_tweets
Playfair, W. (1801). The statistical breviary: shewing the resources of every state and kingdom. London: T. Bensley. Retrieved from http://archive.org/details/statisticalbrev00playgoog. New edition on Amazon
Srivastava, T. N., & Rego, S. (2011). Business Research Methodology. New Delhi: Tata McGraw-Hill.