What Name Is Given to a Statistical Graph That Is Embellished With Additional Art Work

Circular statistical graph that is divisible into slice to illustrate numerical proportion

Pie chart of populations of English native speakers

A pie chart (or a circumvolve chart) is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central bending and area) is proportional to the quantity information technology represents. While information technology is named for its resemblance to a pie which has been sliced, there are variations on the mode it can exist presented. The earliest known pie nautical chart is generally credited to William Playfair's Statistical Breviary of 1801.^{[i] [ii]}

Pie charts are very widely used in the business world and the mass media.^[iii] Nevertheless, they have been criticized,^[4] and many experts recommend fugitive them,^{[5] [6] [vii] [8]} as research has shown information technology is difficult to compare different sections of a given pie chart, or to compare information across different pie charts. Pie charts can be replaced in well-nigh cases by other plots such as the bar chart, box plot, dot plot, etc.

History [edit]

The primeval known pie nautical chart is generally credited to William Playfair'due south Statistical Breviary of 1801, in which two such graphs are used.^{[1] [2] [ix]} Playfair presented an illustration, which contained a serial of pie charts. 1 of those charts depicted the proportions of the Turkish Empire located in Asia, Europe and Africa before 1789. This invention was not widely used at showtime.^[ane]

Playfair thought that pie charts were in need of a tertiary dimension to add boosted information.^[10]

Florence Nightingale may not have invented the pie chart, but she adapted it to go far more readable, which fostered its wide use, still today. Indeed, Nightingale reconfigured the pie chart making the length of the wedges variable instead of their width. The graph, then, resembled a cock's comb.^[11] She was later assumed to accept created it due to the obscurity and lack of practicality of Playfair'due south creation.^[12] Nightingale's polar expanse diagram,^{[13] : 107} or occasionally the Nightingale rose diagram, equivalent to a modern circular histogram, to illustrate seasonal sources of patient mortality in the war machine field hospital she managed, was published in Notes on Matters Affecting the Wellness, Efficiency, and Hospital Administration of the British Regular army and sent to Queen Victoria in 1858. According to the historian Hugh Small, "she may accept been the commencement to use [pie charts] for persuading people of the need for change."^[11]

The French engineer Charles Joseph Minard too used pie charts, in 1858. A map of his from 1858 used pie charts to represent the cattle sent from all around France for consumption in Paris.

Early types of pie charts in the 19th century

• 

  Pie charts from William Playfair's "Statistical Breviary", 1801

• 

  One of the pie charts, 1801

• 

  Minard'southward map, 1858

Variants and similar charts [edit]

3D pie chart and perspective pie cake [edit]

A 3d pie chart, or perspective pie nautical chart, is used to give the chart a 3D expect. Frequently used for aesthetic reasons, the 3rd dimension does non 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 employ of superfluous dimensions not used to display the data of interest is discouraged for charts in full general, non only for pie charts.^{[7] [14]}

Doughnut nautical chart [edit]

Information on the information as a pigsty in the eye of a doughnut chart

A doughnut chart (also spelled donut) is a variant of the pie chart, with a blank middle assuasive for additional information about the data as a whole to be included. ^{[15] [xvi]} Doughnut charts are similar to pie charts in that their aim is to illustrate proportions.^{[ citation needed ]} This blazon of circular graph tin can back up multiple statistics at once and it provides a amend information intensity ratio to standard pie charts.^[16] It does non accept to contain information in the center.

Exploded pie nautical chart [edit]

Exploded pie chart for the example information (see below), with the largest party group exploded.

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

Polar area diagram [edit]

"Diagram of the causes of mortality in the ground forces in the East" past Florence Nightingale.

The polar expanse diagram is like to a usual pie chart, except sectors have equal angles and differ rather in how far each sector extends from the center of the circumvolve. The polar area diagram is used to plot cyclic phenomena (east.g., counts of deaths past month). For example, if the counts of deaths in each month for a year are to be plotted then there volition exist 12 sectors (one per calendar month) all with the aforementioned angle of xxx degrees each. The radius of each sector would be proportional to the foursquare root of the expiry rate for the month, then the expanse of a sector represents the rate of deaths in a month. If the death charge per unit in each month is subdivided past cause of decease, it is possible to make multiple comparisons on one diagram, as is seen in the polar area diagram famously developed by Florence Nightingale.

The first known utilise of polar surface area diagrams was past André-Michel Guerry, which he called courbes circulaires (round curves), in an 1829 paper showing seasonal and daily variation in air current direction over the twelvemonth and births and deaths by hour of the twenty-four hour period.^[17] Léon Lalanne afterwards used a polar diagram to evidence the frequency of wind directions around compass points in 1843. The wind rose is notwithstanding used by meteorologists. Nightingale published her rose diagram in 1858. Although the name "coxcomb" has come to be associated with this type of diagram, Nightingale originally used the term to refer to the publication in which this diagram showtime appeared—an attending-getting book of charts and tables—rather than to this specific type of diagram.^[xviii]

Ring chart, sunburst nautical chart, and multilevel pie chart [edit]

Multi-level pie chart representing disk usage in a Linux file arrangement

A ring nautical chart, likewise known as a sunburst chart or a multilevel pie chart, is used to visualize hierarchical data, depicted by concentric circles.^[19] The circle in the center represents the root node, with the bureaucracy moving outward from the center. A segment of the inner circumvolve bears a hierarchical relationship to those segments of the outer circle which lie within the angular sweep of the parent segment.^[20]

Spie chart [edit]

A spie chart comparing number of students with educatee costs across 4 different schools

A variant of the polar area chart is the spie chart, designed by Dror Feitelson.^[21] The design superimposes a normal pie chart with a modified polar area chart to let the comparison of two sets of related data. The base pie chart represents the first information set in the usual way, with different slice sizes. The second fix is represented by the superimposed polar area chart, using the aforementioned angles every bit the base, and adjusting the radii to fit the data. For instance, the base pie chart could show the distribution of age and gender groups in a population, and the overlay their representation among road casualties. Age and gender groups that are especially susceptible to existence involved in accidents then stand out every bit slices that extend across the original pie chart.

Foursquare chart / Waffle chart [edit]

Square pie chart (waffle chart), showing how smaller percentages are more easily shown than on circular charts. On the 10x10 grid, each cell represents 1%.

Foursquare charts, also called waffle charts, are a course of pie charts that utilise squares instead of circles to represent percentages. Similar to basic round pie charts, square pie charts take each percentage out of a total 100%. They are often x past 10 grids, where each prison cell represents 1%. Despite the proper name, circles, pictograms (such equally of people), and other shapes may be used instead of squares. One major benefit to square charts is that smaller percentages, difficult to see on traditional pie charts, can be easily depicted.^[22]

Example [edit]

A pie nautical chart for the case data

The following case chart is based on preliminary results of the ballot for the European Parliament in 2004. The table lists the number of seats allocated to each party group, along with the derived percentage of the total that they each brand up. The values in the final column, the derived central angle of each sector, Is establish past multiplying the percentage by 360°.

Grouping	Seats	Percent (%)	Central angle (°)
EUL	39	5.three	19.2
Human foot	200	27.three	98.4
EFA	42	five.7	20.seven
EDD	15	2.0	7.iv
ELDR	67	9.2	33.0
EPP	276	37.7	135.seven
UEN	27	3.7	xiii.3
Other	66	9.0	32.5
Full	732	99.9*	360.ii*

*Because of rounding, these totals practice non add upward 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 case, the central angle for the largest group (European People's Party (EPP)) is 135.seven° because 0.377 times 360, rounded to one decimal place, equals 135.vii.

Use and effectiveness [edit]

3D pie chart showing Atmospheric air components percentage

A flaw exhibited by pie charts is that they cannot show more than a few values without separating the visual encoding (the "slices") from the data they represent (typically percentages). When slices become too small, pie charts have to rely on colors, textures or arrows then the reader can understand them. This makes them unsuitable for use with larger amounts of data. Pie charts also take upwardly a larger corporeality of space on the folio compared to the more flexible bar charts, which practice non need to have separate legends, and can display other values such every bit averages or targets at the same time.^[7]

Statisticians generally regard pie charts as a poor method of displaying information, and they are uncommon in scientific literature. I reason is that information technology is more difficult for comparisons to be made between the size of items in a chart when area is used instead of length and when dissimilar items are shown as different shapes.^[23]

Three sets of percentages, plotted as both piecharts and barcharts. Comparing the data on barcharts is by and large easier.

Further, in research performed at AT&T Bell Laboratories, information technology was shown that comparison past angle was less accurate than comparison by length. About subjects accept difficulty ordering the slices in the pie chart by size; when an equivalent bar nautical chart is used the comparing is much easier.^[24] Similarly, comparisons between data sets are easier using the bar nautical chart. However, if the goal is to compare a given category (a slice of the pie) with the full (the whole pie) in a single nautical chart and the multiple is close to 25 or fifty percent, so a pie chart tin often be more constructive than a bar graph.^{[25] [26]}

An example of a pie chart with xviii values, with some colors repeated

In a pie chart with many department, several values may be represented with the aforementioned or similar colors, making interpretation difficult.

An example of a doughnut shape pie chart, showing the batting and run records of Indian cricket players in test matches in 2019

Several studies presented at the European Visualization Briefing analyzed the relative accuracy of several pie chart formats,^{[27] [28] [22]} reaching the determination that pie charts and doughnut charts produce similar fault levels when reading them, and foursquare pie charts provide the near accurate reading.^[29]

References [edit]

1. ^ ^{a b c} Spence (2005)
2. ^ ^{a b} Tufte, p. 44
3. ^ Cleveland, p. 262
4. ^ Wilkinson, p. 23.
5. ^ Tufte, p. 178.
6. ^ van Belle, p. 160–162.
7. ^ ^{a b c} Stephen Few. "Salvage the Pies for Dessert", August 2007, Retrieved 2010-02-02
8. ^ Steve Fenton "Pie Charts Are Bad"
9. ^ "Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization". www.datavis.ca.
10. ^ Palsky, p. 144–145
11. ^ ^{a b} Greenbaum, Hilary; Rubinstein, Dana (20 April 2012). "Who Made That Pie Chart?". The New York Times.
12. ^ Dave commodity on this data on QI
13. ^ Cohen, I. Bernard (March 1984). "Florence Nightingale". Scientific American. 250 (3): 128–137. Bibcode:1984SciAm.250c.128C. doi:10.1038/scientificamerican0384-128. PMID 6367033. (alternative pagination depending on state of sale: 98–107, bibliography on p. 114) online article – run into documents link at left
14. ^ Skillful and Hardin, chapter viii.
15. ^ Harris, Robert 50. (1999). Information graphics : a comprehensive illustrated reference ([Nachdr.] ed.). Oxford: Oxford University Press. p. 143. ISBN9780195135329.
16. ^ ^{a b} Information Design by Juergen Kai-Uwe Brock on iBooks. iBooks . Retrieved 2017-06-10 .
17. ^ Friendly, p. 509
18. ^ "Florence Nightingale's Statistical Diagrams". Retrieved 2010-11-22 .
19. ^ "Multi-level Pie Charts". www.neoformix.com.
20. ^ Webber Richard, Herbert Ric, Jiangbc Wel. "Infinite-filling Techniques in Visualizing Output from Computer Based Economical Models"
21. ^ "Feitelson, Dror (2003) Comparing Partitions With Spie Charts" (PDF). 2003. Retrieved 2010-08-31 .
22. ^ ^{a b} Kosara, Robert; Skau, Drew (2016). "Judgment Error in Pie Chart Variations". EuroVis.
23. ^ Krygier, John (28 August 2007). "Perceptual Scaling of Map Symbols". makingmaps.net . Retrieved 3 May 2015.
24. ^ Cleveland, p. 86–87
25. ^ Simkin, D., & Hastie, R. (1987). An Information-Processing Analysis of Graph Perception. Journal of the American Statistical Association, 82(398), 454. doi:10.2307/2289447. Kosara, Robert (13 April 2011). "In Defence of Pie Charts". Retrieved April 13, 2011.
26. ^ Spence, Ian; Lewandowsky, Stephan (1 January 1991). "Displaying proportions and percentages". Applied Cognitive Psychology. 5 (1): 61–77. doi:x.1002/acp.2350050106.
27. ^ "An Illustrated Tour of the Pie Chart Study Results". eagereyes. 2016-06-28. Retrieved 2016-11-28 .
28. ^ Skau, Drew; Kosara, Robert (2016). "Arcs, Angles, or Areas: Individual Information Encodings in Pie and Donut Charts". EuroVis.
29. ^ "A Reanalysis of A Report About (Square) Pie Charts from 2009". eagereyes. 2016-07-xi. Retrieved 2016-xi-28 .

Farther reading [edit]

• Cleveland, William S. (1985). The Elements of Graphing Data. Pacific Grove, CA: Wadsworth & Advanced Book Program. ISBN0-534-03730-5.
• Friendly, Michael. "The Golden Age of Statistical Graphics," Statistical Science, Volume 23, Number four (2008), 502-535
• Good, Phillip I. and Hardin, James Westward. Common Errors in Statistics (and How to Avoid Them). Wiley. 2003. ISBN 0-471-46068-0.
• Guerry, A.-1000. (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. ISBN0-19-513532-vi.
• Lima, Manuel. "Why humans love pie charts: an historical and evolutionary perspective," Noteworthy, July 23, 2018
• 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 Academy Press (2005) ISBN 0-521-85554-three.
• 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 Data. Graphics Press, 2001. ISBN 0-9613921-4-2.
• Van Belle, Gerald. Statistical Rules of Pollex. Wiley, 2002. ISBN 0-471-40227-3.
• Wilkinson, Leland. The Grammar of Graphics, 2nd edition. Springer, 2005. ISBN 0-387-24544-viii.

External links [edit]

Wikimedia Eatables has media related to Pie charts.

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Source: https://en.wikipedia.org/wiki/Pie_chart

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