Can the percentages in a pie chart add up to more than $100\%$ and the data or analyses will still make sense (or be logical)? Let's say the percentage in a pie chart adds up to $100\%$ . Does this make statistical sense?

# Solved – Can the percentages in a pie chart add up to more than $100\%$ and the data or analyses will still make sense (or be logical)

pie chart

#### Related Solutions

I wouldn't say there's an increasing interest or debate about the use of pie charts. They are just found everywhere on the web and in so-called "predictive analytic" solutions.

I guess you know Tufte's work (he also discussed the use of multiple pie charts), but more funny is the fact that the second chapter of Wilkinson's *Grammar of Graphics* starts with "How to make a pie chart?".
You're probably also aware that Cleveland's dotplot, or even a barchart, will convey much more precise information. The problem seems to really stem from the way our visual system is able to deal with spatial information. It is even quoted in the R software; from the on-line help for `pie`

,

Cleveland (1985), page 264: “Data that can be shown by pie charts always can be shown by a dot chart. This means that judgements of position along a common scale can be made instead of the less accurate angle judgements.” This statement is based on the empirical investigations of Cleveland and McGill as well as investigations by perceptual psychologists.

Cleveland, W. S. (1985)

The elements of graphing data. Wadsworth: Monterey, CA, USA.

There are variations of pie charts (e.g., donut-like charts) that all raise the same problems: We are not good at evaluating angle and area. Even the ones used in "corrgram", as described in Friendly, Corrgrams: Exploratory displays for correlation matrices, *American Statistician* (2002) 56:316, are hard to read, IMHO.

At some point, however, I wondered whether they might still be useful, for example (1) displaying two classes is fine but increasing the number of categories generally worsen the reading (especially with strong imbalance between %), (2) relative judgments are better than absolute ones, that is displaying two pie charts side by side should favor a better appreciation of the results than a simple estimate from, say a pie chart mixing all results (e.g. a two-way cross-classification table). Incidentally, I asked a similar question to Hadley Wickham who kindly pointed me to the following articles:

- Spence, I. (2005). No Humble Pie: The Origins and Usage of a Statistical Chart.
*Journal of Educational and Behavioral Statistics*, 30(4), 353–368. - Heer, J. and Bostock, M. (2010). Crowdsourcing Graphical Perception: Using Mechanical Turk to Assess Visualization Design.
*CHI 2010*, April 10–15, 2010, Atlanta, Georgia, USA.

In sum, I think they are just good for grossly depicting the distribution of 2 to 3 classes (I use them, from time to time, to show the distribution of males and females in a sample on top of an histogram of ages), but they must be accompanied by relative frequencies or counts for being really informative. A table would still do a better job since you can add margins, and go beyond 2-way classifications.

Finally, there are alternative displays that are built upon the idea of pie chart. I can think of square pie or waffle chart, described by Robert Kosara in Understanding Pie Charts.

It might be easier than I thought -- please let me know if this is correct or on the right path.

Let's assume the following data:

- Company A: 70 percentage of capture across 10 contracts
- Company B: 60 percentage of capture across 100 contracts
- Company C: 50 percentage of capture across 40 contracts

First, I figured out the percentage of each contractors contribution to the total amount of contracts, so:

- Company A: 6.67% of total contracts
- Company B: 66.67% of total contracts
- Company C: 26.67% of total contracts

I then took the company's capture rate and multiplied it by their percentage of total contracts, so:

- Company A: 4.67% contributing to total percentage
- Company B: 40% contributing to total percentage
- Company C: 13.33% of contributing to total percentage

Which makes the total:

- 58.00% across 150 contracts

Please let me know if this is correct (or close enough). Thanks!

## Best Answer

If the real numbers add up to 100%, and the difference is just round-off error, then it's okay, but I would include a note in the legend to explain.

If the numbers are not proportions of some whole, then you shouldn't use a pie chart. (And I'm not alone in thinking that you should find an alternative to a pie chart in any case.)