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mathematics

Radar chart

Radar 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 Radar chart rather than just read about it. In short: A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. The relative position and angle of the axes is typically uninformative, but various heuristics, such as algorithms that plot data as the maximal total area, can be applied to sort the variables (axes) into relative positio…

Radar chart — main illustration
Radar chart — illustration

Key takeaways

  • Radar 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 Radar chart to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Radar chart from memory before moving on to harder problems.

Reference excerpt

A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. The relative position and angle of the axes is typically uninformative, but various heuristics, such as algorithms that plot data as the maximal total area, can be applied to sort the variables (axes) into relative positions that reveal distinct correlations, trade-offs, and a multitude of other comparative measures. Radar charts are also known as web charts, spider charts, spider graphs, spider web charts, star charts, star plots, cobweb charts, irregular polygons, polar charts, and Kiviat diagrams. It is equivalent to a parallel coordinates plot, with the axes arranged radially.

Overview The radar chart is a chart and/or plot that consists of a sequence of equi-angular spokes, called radii, with each spoke representing one of the variables. The data length of a spoke is proportional to the magnitude of the variable for the data point relative to the maximum magnitude of the variable across all data points. A line is drawn connecting the data values for each spoke. This gives the plot a star-like appearance and the origin of one of the popular names for this plot. The star plot can be used to answer the following questions:

Which observations are most similar, i.e., are there clusters of observations? (Radar charts are used to examine the relative values for a single data point (e.g., point 3 is large for variables 2 and 4, small for variables 1, 3, 5, and 6) and to locate similar points or dissimilar points.) Are there outliers? Radar charts are a useful way to display multivariate observations with an arbitrary number of variables. Each star represents a single observation. Typically, radar charts are generated in a multi-plot format with many stars on each page and each star representing one observation. The star plot was first used by Georg von Mayr in 1877. Radar charts differ from glyph plots in that all variables are used to construct the plotted star figure. There is no separation into foreground and background variables. Instead, the star-shaped figures are usually arranged in a rectangular array on the page. It is somewhat easier to see patterns in the data if the observations are arranged in some non-arbitrary order (if the variables are assigned to the rays of the star in some meaningful order).

Applications

Radar charts can be used in sports to chart players' strengths and weaknesses by calculating various statistics related to the player that can tracked along the central axis of the chart. Examples include a basketball players shots made, rebounds, assists, etc., or the batting or pitching stats of a baseball player. This creates a centralized visualization of the strengths and weaknesses of a player, and if overlapped with the statistics of other players or league averages, can display where a player excels and where they could improve. These insights into player strengths and weakness could prove crucial to player development as it allows coaches and trainers to adjust a player's training regiment to help improve on their weaknesses. The results of the radar chart can also be useful in situational play. If a batter is shown to hit poorly against left-handed pitching, then his team knows to limit his plate appearances against left-handed pitchers, while the opposing team may try to force a situation where the batter is forced to hit against the pitcher. Another application of radar charts is the control of quality improvement to display the performance metrics various objects including computer programs, computers, phones, vehicles, and more. Computer programmer often use analytics to test the performance of their programs versus others. An example of this where radar charts may be useful is the performance analysis of various sorting algorithms. A programmer could gather up several different sorting algorithms such as selection, bubble, and quick, then analyze the performance of these algorithms by measuring their speed, memory usage, and power usage, then graph these on a radar chart to see how each sort performs under various sizes of data. Another performance application is measuring the performance of similar cars against each other. A consumer could look at variables such as the cars' top speed, miles per gallon, horsepower, and torque. Then after using a radar chart to visualize the data, they could decide on what car is best for them based on the results.

Radar charts can be used in life sciences to display the strengths and weakness of drugs and other medications. Using the example of two anti-depressants, a researcher can rank variables such as efficacy, side effects, cost, etc. on a scale of one to ten. They could then graph the results using a radar chart to see the spread of variables and find how the differ, such as one anti-depressant being cheaper and quicker acting, but not having great relief over time. Meanwhile, the other anti-depressant provides stronger relief and holds up better over time but is more expensive. Another life science application is in patient analysis. Radar charts can be used to graph the variables of life affecting a person's wellness, and then be analyzed to help them. A more specific example is in the case of athletes, whose various wellness habits such as sleep, diet, and stress are monitored to make sure they stay in peak physical condition. If any areas would be shown dipping, doctors and trainers could step in to assist the athlete and improve their wellness.

… excerpt ends here. Continue reading the full article.

Illustrations

Radar chart: Example star plot from NASA, with some of the most desirable design results represented in the center
Example star plot from NASA, with some of the most desirable design results represented in the center
Radar chart: This spider chart represents the allocated budget versus actual spending for a given organization.
This spider chart represents the allocated budget versus actual spending for a given organization.
Radar chart: A radar chart showing batting statistics from the 2021 MLB season. Shohei Ohtani, green, outperforms the DH, red, and MLB, blue, averages for that season, but also strikes out more often. Data from https://www.baseball-reference.com/.
A radar chart showing batting statistics from the 2021 MLB season. Shohei Ohtani, green, outperforms the DH, red, and MLB, blue, averages for that season, but also strikes out more often. Data from https://www.baseball-reference.com/.
Radar chart: A radar chart showing the differences in performance metrics of a sedan, sports car, and pickup truck.
A radar chart showing the differences in performance metrics of a sedan, sports car, and pickup truck.
Radar chart: A radar chart showing the similarity of two communities that consist of connected genomic windows; see genome architecture mapping.
A radar chart showing the similarity of two communities that consist of connected genomic windows; see genome architecture mapping.

Worked examples

Example 1 — a first encounter with Radar chart

Start with the simplest possible case. Write down what Radar 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 Radar 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 Radar 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 Radar chart

In research
Radar 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 Radar 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
Radar chart is common in secondary-school and first-year university syllabi. It links to neighbouring topics Charts, Statistical charts and diagrams, so understanding it makes those chapters shorter.
In everyday life
Look for Radar 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 Radar chart in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Radar 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 Radar chart out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Radar chart in simple terms?

A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. The relative position and angle of the axes is typically uninformative, but various heuristics, such a…

Why does Radar 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 Radar 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 Radar chart.

Tags

  • Charts
  • Statistical charts and diagrams

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