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mathematics

Pie chart

Pie chart is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Pie chart rather than just read about it. In short: A pie chart (or a circle 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 angle and area) is proportional to the quantity it represents.

Pie chart — main illustration
Pie chart — illustration

Key takeaways

  • Pie chart belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Pie chart to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Pie chart from memory before moving on to harder problems.

Reference excerpt

A pie chart (or a circle 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 angle and area) is proportional to the quantity it represents. While it is named for its resemblance to a pie which has been sliced, there are variations on the way it can be presented. The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801. Pie charts are very widely used in the business world and the mass media. However, they have been criticized, and many experts recommend avoiding them, as research has shown it is more difficult to make simple comparisons such as the size of different sections of a given pie chart, or to compare data across different pie charts. Some research has shown pie charts perform well for comparing complex combinations of sections (e.g., "A + B vs. C + D"). Commonly recommended alternatives to pie charts in most cases include bar charts, box plots, and dot plots.

History The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801, in which two such graphs are used. Playfair presented an illustration, which contained a series of pie charts. One 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 first. Playfair thought that pie charts were in need of a third dimension to add additional information. Florence Nightingale may not have invented the pie chart, but she adapted it to make it more readable, which fostered its wide use, still today. Nightingale reconfigured the pie chart making the length of the wedges variable instead of their width. The graph, then, resembled a cock's comb. She was later assumed to have created it due to the obscurity and lack of practicality of Playfair's creation. Nightingale's polar area diagram, or occasionally the Nightingale rose diagram, equivalent to a modern circular histogram, to illustrate seasonal sources of patient mortality in the military field hospital she managed, was published in Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army and sent to Queen Victoria in 1858. According to the historian Hugh Small, "she may have been the first to use [pie charts] for persuading people of the need for change." The French engineer Charles Joseph Minard also 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.

Variants and similar charts

3D pie chart and perspective pie cake A 3D pie chart, or perspective pie chart, is used to give the chart a 3D look. 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.

Doughnut chart

A doughnut chart (also spelled donut) is a variant of the pie chart, with a blank center allowing for additional information about the data as a whole to be included. Doughnut charts are similar to pie charts in that their aim is to illustrate proportions. This type of circular graph can support multiple statistics at once and it provides a better data intensity ratio than standard pie charts. It does not have to contain information in the center.

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.

Polar area diagram

The polar area diagram is similar to a usual pie chart, except sectors have equal angles and differ rather in how far each sector extends from the center of the circle. It is used to plot cyclic phenomena (e.g., counts of deaths by month). For example, if the counts of deaths in each month for a year are to be plotted then there will be 12 sectors (one per month) all with the same angle of 30 degrees each. The radius of each sector would be proportional to the square root of the death rate for the month, so the area of a sector represents the rate of deaths in a month. If the death rate in each month is subdivided by cause of death, 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 use of polar area diagrams was by André-Michel Guerry, which he called courbes circulaires (circular curves), in an 1829 paper showing seasonal and daily variation in wind direction over the year and births and deaths by hour of the day. Léon Lalanne later used a polar diagram to show the frequency of wind directions around compass points in 1843. The wind rose is still 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 first appeared—an attention-getting book of charts and tables—rather than to this specific type of diagram.

Ring chart, sunburst chart, and multilevel pie chart

A ring chart, also known as a sunburst chart or a multilevel pie chart, is used to visualize hierarchical data, depicted by concentric circles. The circle in the center represents the root node, with the hierarchy moving outward from the center. 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.

Spie chart

… excerpt ends here. Continue reading the full article.

Illustrations

Pie chart: Pie chart of populations of English native speakers
Pie chart of populations of English native speakers
Pie chart illustration
Pie chart illustration
Pie chart illustration
Pie chart illustration

Worked examples

Example 1 — a first encounter with Pie chart

Start with the simplest possible case. Write down what Pie chart claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Pie chart before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Pie chart ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Pie chart

In research
Pie chart appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Pie chart in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Pie chart is common in secondary-school and first-year university syllabi. It links to neighbouring topics Statistical charts and diagrams, so understanding it makes those chapters shorter.
In everyday life
Look for Pie chart outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Pie chart in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Pie chart means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Pie chart out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pie chart in simple terms?

A pie chart (or a circle 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 angle and area) is proportional to the quantity it represents.

Why does Pie chart matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Pie chart?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Pie chart.

Tags

  • Statistical charts and diagrams

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