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Statistical graphics

Statistical graphics 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 Statistical graphics rather than just read about it. In short: Statistical graphics, also known as statistical graphical techniques, are graphics used in the field of statistics for data visualization. Overview Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form.

Statistical graphics — main illustration
Statistical graphics — illustration

Key takeaways

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

Reference excerpt

Statistical graphics, also known as statistical graphical techniques, are graphics used in the field of statistics for data visualization.

Overview Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form. They include plots such as scatter plots, histograms, probability plots, spaghetti plots, residual plots, box plots, block plots and biplots. Exploratory data analysis (EDA) relies heavily on such techniques. They can also provide insight into a data set to help with testing assumptions, model selection and regression model validation, estimator selection, relationship identification, factor effect determination, and outlier detection. In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others. Graphical statistical methods have four objectives:

The exploration of the content of a data set The use to find structure in data Checking assumptions in statistical models Communicate the results of an analysis. If one is not using statistical graphics, then one is forfeiting insight into one or more aspects of the underlying structure of the data.

History Statistical graphics have been central to the development of science and date to the earliest attempts to analyse data. Many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper were used in the 18th century. Statistical graphics developed through attention to four problems:

Spatial organization in the 17th and 18th century Discrete comparison in the 18th and early 19th century Continuous distribution in the 19th century and Multivariate distribution and correlation in the late 19th and 20th century. Since the 1970s statistical graphics have been re-emerging as an important analytic tool with the revitalisation of computer graphics and related technologies.

Examples

Famous graphics were designed by:

William Playfair who produced what could be called the first line, bar, pie, and area charts. For example, in 1786 he published the well known diagram that depicts the evolution of England's imports and exports, James Watt and his employee John Southern, who around 1790 invented the steam indicator, a device for plotting pressure variations within a steam engine cylinder through its stroke, Florence Nightingale, who used statistical graphics to persuade the British Government to improve army hygiene, John Snow who plotted deaths from cholera in London in 1854 to detect the source of the disease, and Charles Joseph Minard who designed a large portfolio of maps of which the one depicting Napoleon's campaign in Russia is the best known. See the plots page for many more examples of statistical graphics.

See also Data and information visualization List of graphical methods Visual inspection Chart List of charting software

References Citations

Attribution This article incorporates public domain material from the National Institute of Standards and Technology

Further reading Cleveland, W. S. (1993). Visualizing Data. Summit, NJ, USA: Hobart Press. ISBN 0-9634884-0-6. Cleveland, W. S. (1994). The Elements of Graphing Data. Summit, NJ, USA: Hobart Press. ISBN 0-9634884-1-4. Lewi, Paul J. (2006). Speaking of Graphics. Tufte, Edward R. (2001) [1983]. The Visual Display of Quantitative Information (2nd ed.). Cheshire, CT, USA: Graphics Press. ISBN 0-9613921-4-2. Tufte, Edward R. (1992) [1990]. Envisioning Information. Cheshire, CT, USA: Graphics Press. ISBN 0-9613921-1-8.

External links

Trend Compass Alphabetic gallery of graphical techniques DataScope a website devoted to data visualization and statistical graphics

Illustrations

Statistical graphics illustration
Statistical graphics: William Playfair's trade-balance time-series chart, published in his Commercial and Political Atlas, 1786
William Playfair's trade-balance time-series chart, published in his Commercial and Political Atlas, 1786
Statistical graphics: John Snow's Cholera map in dot style, 1854
John Snow's Cholera map in dot style, 1854

Worked examples

Example 1 — a first encounter with Statistical graphics

Start with the simplest possible case. Write down what Statistical graphics 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 Statistical graphics 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 Statistical graphics 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 Statistical graphics

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

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

Frequently asked questions

What is Statistical graphics in simple terms?

Statistical graphics, also known as statistical graphical techniques, are graphics used in the field of statistics for data visualization. Overview Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be…

Why does Statistical graphics 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 Statistical graphics?

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 Statistical graphics.

Tags

  • Infographics
  • Statistical charts and diagrams

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