# Pie chart

Pie chart of populations of English native speakers

A pie chart (or a circle graph) is a circular chart divided into sections, illustrating relative magnitudes or frequencies. In a pie chart, the arc length of each section (and consequently its central angle and area), is proportional to the quantity it represents. Together, the sections create a full disk. It is named for its resemblance to a pie that has been sliced.

While the pie chart is perhaps the most ubiquitous statistical chart in the business world and the mass media, it is rarely used in scientific or technical publications.[1] It is one of the most widely criticized charts,[2] and many statisticians recommend to avoid its use altogether[3][4], pointing out in particular that it is difficult to compare different sections of a given pie chart, or to compare data across different pie charts. Pie charts can be an effective way of displaying information in some cases, in particular if the intent is to compare the size of a slice with the whole pie, rather than comparing the slices among them.[5] Pie charts work particularly well when the slices represent 25 or 50% of the data,[6] but in general, other plots such as the bar chart or the dot plot, or non-graphical methods such as tables, may be more adapted for representing information.

The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801.[5][7]

## Example

A pie chart for the example data.
An exploded pie chart for the example data, with the largest party group exploded.

The following example chart is based on preliminary results of the election for the European Parliament in 2004. The following table lists the number of seats allocated to each party group, along with the derived percentage of the total that they each make up. The values in the last column, the derived central angle of each sector, is found by multiplying the percentage by 360°.

Group Seats Percent (%) Central angle (°)
EUL 39 5.3 19.2
PES 200 27.3 98.4
EFA 42 5.7 20.7
EDD 15 2.0 7.4
ELDR 67 9.2 33.0
EPP 276 37.7 135.7
UEN 27 3.7 13.3
Other 66 9.0 32.5
Total 732 99.9* 360.2*

* Because of rounding, these totals do not add up to 100 and 360.

The size of each central angle is proportional to the size of the corresponding quantity, here the number of seats. Since the sum of the central angles has to be 360°, the central angle for a quantity that is a fraction Q of the total is 360Q degrees. In the example, the central angle for the largest group (European People's Party|EPP) is 135.7° because 0.377 times 360, rounded to one decimal place(s), equals 135.7.

## Criticism

Three sets of data plotted using pie charts and bar charts.

Statisticians tend to regard pie charts as a poor method of displaying information. While pie charts are common in business and journalism, they are uncommon in scientific literature. One reason for this is that it is more difficult for comparisons to be made between the size of items in a chart when area is used instead of length. In Stevens' power law, visual area is perceived with a power of 0.7, compared to a power of 1.0 for length. This suggests that length is a better scale to use, since perceived differences would be linearly related to actual differences.

In research performed at AT&T Bell Laboratories, it was shown that comparison by angle was less accurate than comparison by length. This can be illustrated with the diagram to the right, showing three pie charts, and, below each of them, the corresponding bar chart representing the same data. Most subjects have difficulty ordering the slices in the pie chart by size; when the bar chart is used the comparison is much easier. [8]. Similarly, comparisons between datasets are easier using the barchart. However, if the goal is to compare a given category (a slice of the pie) with the total (the whole pie) in a single chart and the multiple is close to 25% or 50%, then a pie chart can often be more effective than a bar graph.

## Variants and similar charts

"Diagram of the causes of mortality in the army in the East" by Florence Nightingale.

### Polar Area Pie Chart

Florence Nightingale is credited with developing a form of the pie chart now known as the polar area diagram, or occasionally the Nightingale rose diagram and first published in 1858. The name "coxcomb" is sometimes used erroneously. This was the name Nightingale used to refer to a book containing the diagrams rather than the diagrams themselves.[9]

The polar area diagram is similar to a usual pie chart, except that the sectors are each of an equal angle and differ rather in how far each sector extends from the centre of the circle, enabling multiple comparisons on one diagram. It has been suggested that most of Nightingale's early reputation was built on her ability to give clear and concise presentations of data.

Although Florence Nightingale is usually credited with this graphical invention, there are earlier uses. Léon Lalanne used a polar diagram to show the frequency of wind directions around compass points in 1843. André-Michel Guerry is an earlier inventor of the "rose diagram" form, in an 1829 paper showing frequency of events for cyclic phenomena.[citation needed]

### Multi-level Pie Chart

Multi-level pie chart, also known as a radial tree chart is an information visualization technique which is used for representing hierarchical data.[10] The hierarchical structure of data is depicted by means of concentric circles. The circle in the centre represents the root node, with the herrarchy moving outward from the centre. A segment of the inner circle bears a hierarchical relationship to those segments of the outer circle which lie within the angular sweep of the parent segment.[11]

The multi-level pie chart was originally devised for visually depicting space filling of computer storage systems. The concept was originally termed as SunBurst technique. Later however, this technique was adopted for business and economics. Owing to its resemblance to the standard pie chart - the SunBurst technique, eventually became popular as multi-level pie chart.[12]

The multi-level pie chart is an efficient business analysis tool. It is highly suited for visualizing the performance of the marketing channel. Additionally, it can even be deployed for monitoring resource allocation and revenue mapping.[13]

### Exploded Pie Chart

A chart with one or more sectors separated from the rest of the disk is known as an exploded pie chart. This effect is used to either highlight a sector, or to highlight smaller segments of the chart with small proportions.

### 3D Pie Chart

A perspective (3D) pie chart is used to give the chart a 3D look-and-feel. Often used for aesthetic reasons, the third dimension does not improve the reading of the data; on the contrary, these plots are difficult to interpret because of the distorted effect of perspective associated with the third dimension. The use of superfluous dimensions not used to display the data of interest is discouraged for charts in general, not only for pie charts.[14]

### Doughnut Chart

A doughnut chart, also called a Donut chart is functionally identical to a standard pie chart, with the exception of a blank center.

## History

The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801, where two such graphs are used.[5][7] This invention was not widely used at first;[5] Charles Joseph Minard being one of the first to use it in 1858, in particular in maps where he needs to add information in a third dimension.[15]

• Pro-rata

## Notes

1. Cleveland, p. 262
2. Wilkinson, p. 23.
3. Tufte, p. 178.
4. van Belle, p. 160–162.
5. Spence (2005)
6. Good and Hardin, p. 117–118.
7. Tufte, p. 44
8. Cleveland, p. 86–87
9. "Florence Nightingale's Statistical Diagrams". Florence Nightingale Museum. Retrieved 2006-11-21.
10. Clark Jeff. (2006). ‘’Neoformix’’. Multi-level Pie Charts
11. [Webber Richard, Herbert Ric, Jiangbc Wel. Space-filling Techniques in Visualizing Output from Computer Based Economic Models]
13. ‘’The FusionCharts Blog’’. Second base with charts: Understanding the Multi-level pie chart
14. Good and Hardin, chapter 8.
15. Palsky, p. 144–145

## References

• Cleveland, William S. (1985). The Elements of Graphing Data. Pacific Grove, CA: Wadsworth & Advanced Book Program. ISBN 0-534-03730-5.
• Good, Phillip I. and Hardin, James W. Common Errors in Statistics (and How to Avoid Them). Wiley. 2003. ISBN 0-471-46068-0.
• Guerry, A.-M. (1829). Tableau des variations météorologique comparées aux phénomènes physiologiques, d'aprés les observations faites à l'obervatoire royal, et les recherches statistique les plus récentes. Annales d'Hygiène Publique et de Médecine Légale , 1 :228-.
• Harris, Robert L. (1999). Information Graphics: A comprehensive Illustrated Reference. Oxford University Press. ISBN 0-19-513532-6.
• Palsky Gilles. Des chiffres et des cartes: la cartographie quantitative au XIXè siècle. Paris: Comité des travaux historiques et scientifiques, 1996. ISBN 2-7355-0336-4.
• Playfair, William, Commercial and Political Atlas and Statistical Breviary, Cambridge University Press (2005) ISBN 0-521-85554-3.
• Spence, Ian. No Humble Pie: The Origins and Usage of a statistical Chart. Journal of Educational and Behavioral Statistics. Winter 2005, 30 (4), 353–368.
• Tufte, Edward. The Visual Display of Quantitative Information. Graphics Press, 2001. ISBN 0961392142.
• van Belle, Gerald. Statistical Rules of Thumb. Wiley, 2002. ISBN 0471402273.
• Wilkinson, Leland. The Grammar of Graphics, 2nd edition. Springer, 2005. ISBN 0-387-24544-8.
• Clark Jeff. (2006). ‘’Neoformix’’. Multi-level Pie Charts [1]
• Webber Richard, Herbert Ric, Jiangbc Wel. Space-filling Techniques in Visualizing Output from Computer Based Economic Models [2]