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A pie chart is a circular chart divided into sectors, illustrating relative magnitudes or frequencies. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. Together, the sectors create a full disk. A chart with one or more sectors separated from the rest of the disk is called an exploded pie chart.
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. It is one of the most widely criticised charts, and many statisticians recommend to avoid its use altogether, 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. While pie charts can be an effective way of displaying information in some cases, in particular when the slices represent 25 or 50% of the data, in general, other plots such as the bar chart or the dot chart are more adapted for representing information.
The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801.
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 percentage of the total that they each make up. The values in the last column, the central angle of each sector, is found by multiplying the percentage by 360°.
|Group||Seats||Percent (%)||Central angle (°)|
*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 (EPP) is 135.7° because 0.377 times 360, rounded to one decimal place, equals 135.7.
Warning against usage
Pie charts should be used only when the sum of all categories is meaningful, for example if they represent proportions.
Pie charts are rare in the scientific literature, but are more common in business and economics. One reason for this may be 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 be 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 a pie chart and a bar chart for the same data side to side. Most subjects have difficulty ordering the slices in the pie chart by size; when the bar chart is used the comparison is much easier. 
Polar area diagram
Florence Nightingale is credited with developing an early form of the pie chart which she first published in 1858. This form of pie chart is now known as the polar area diagram, or occasionally the Nightingale rose diagram. Sometimes "coxcomb" is used erroneously, but this was the name Nightingale used to refer to a book containing the diagrams rather than the diagrams themselves. 
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 sectors extends from the centre of the circle. It has been suggested that most of Nightingale's early reputation was built on her ability to give clear and concise presentations of data.
- Cleveland, p. 262
- Wilkinson, p. 23.
- Tufte, p. 178.
- van Belle, p. 160–162.
- Good and Hardin, p. 117–118.
- Cleveland, p. 86–87
- Florence Nightingale's Statistical Diagrams. Florence Nightingale Museum. URL accessed on 2006-11-21.
- Cleveland, William (1985). The Elements of Graphing Data, Pacific Grove, California: Wadsworth & Advanced Book Program. ISBN 0-534-03730-5.
- Phillip I. Good and James W. Hardin. Common Errors in Statistics (and How to Avoid Them). Wiley. 2003. ISBN 0-471-46068-0.
- Playfair, William, Commercial and Political Atlas and Statistical Breviary, Cambridge University Press (2005) ISBN 0-521-85554-3.
- Edward Tufte. The Visual Display of Quantitative Information. Graphics Press, 2001. ISBN 0961392142.
- Gerald van Belle. Statistical Rules of Thumb. Wiley, 2002. ISBN 0471402273.
- Leland Wilkinson. The Grammar of Graphics, 2nd edition. Springer, 2005. ISBN 0-387-24544-8.
- eu:Sektore diagrama
- he:דיאגרמת עוגה
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