📉Graphical Representation: Perception (Just the Quotes)

"We can gain further insight into what makes good plots by thinking about the process of visual perception. The eye can assimilate large amounts of visual information, perceive unanticipated structure, and recognize complex patterns; however, certain kinds of patterns are more readily perceived than others. If we thoroughly understood the interaction between the brain, eye, and picture, we could organize displays to take advantage of the things that the eye and brain do best, so that the potentially most important patterns are associated with the most easily perceived visual aspects in the display." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"When a graph is constructed, quantitative and categorical information is encoded, chiefly through position, size, symbols, and color. When a person looks at a graph, the information is visually decoded by the person's visual system. A graphical method is successful only if the decoding process is effective. No matter how clever and how technologically impressive the encoding, it is a failure if the decoding process is a failure. Informed decisions about how to encode data can be achieved only through an understanding of the visual decoding process, which is called graphical perception." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Pie charts have severe perceptual problems. Experiments in graphical perception have shown that compared with dot charts, they convey information far less reliably. But if you want to display some data, and perceiving the information is not so important, then a pie chart is fine." (Richard Becker & William S Cleveland," S-Plus Trellis Graphics User's Manual", 1996)

"[...] when data is presented in certain ways, the patterns can be readily perceived. If we can understand how perception works, our knowledge can be translated into rules for displaying information. Following perception‐based rules, we can present our data in such a way that the important and informative patterns stand out. If we disobey the rules, our data will be incomprehensible or misleading." (Colin Ware, "Information Visualization: Perception for Design" 2nd Ed., 2004)

"Most dashboards fail to communicate efficiently and effectively, not because of inadequate technology (at least not primarily), but because of poorly designed implementations. No matter how great the technology, a dashboard's success as a medium of communication is a product of design, a result of a display that speaks clearly and immediately. Dashboards can tap into the tremendous power of visual perception to communicate, but only if those who implement them understand visual perception and apply that understanding through design principles and practices that are aligned with the way people see and think." (Stephen Few, "Information Dashboard Design", 2006)

"Perception requires imagination because the data people encounter in their lives are never complete and always equivocal. [...] We also use our imagination and take shortcuts to fill gaps in patterns of nonvisual data. As with visual input, we draw conclusions and make judgments based on uncertain and incomplete information, and we conclude, when we are done analyzing the patterns, that out picture is clear and accurate. But is it?" (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"[…] perceptual accuracy decreases with distance, so columns that are to be compared should be side by side. Current linked micromap software requires the user." (Daniel B Carr & Linda W Pickle, "Visualizing Data Patterns with Micromaps", 2010)

"Sparklines aren't necessarily a variation on the line chart, rather, a clever use of them. [...] They take advantage of our visual perception capabilities to discriminate changes even at such a low resolution in terms of size. They facilitate opportunities to construct particularly dense visual displays of data in small space and so are particularly applicable for use on dashboards." (Andy Kirk, "Data Visualization: A successful design process", 2012)

"For every rule in data visualization, there is a scenario where that rule should be broken. This means that choosing the best chart or the best design is always a trade-off between several conflicting goals. Our imperfect perception means that data visualization has a larger subjective dimension than a data table. Sometimes we only need this subjective, impressionist dimension and other times we need to translate it into hard figures. Striving for accuracy is important, but it’s more important to provide those insights that only a visual display can reveal." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"Color is difficult to use effectively. A small number of well-chosen colors can be highly distinguishable, particularly for categorical data, but it can be difficult for users to distinguish between more than a handful of colors in a visualization. Nonetheless, color is an invaluable tool in the visualization toolbox because it is a channel that can carry a great deal of meaning and be overlaid on other dimensions. […] There are a variety of perceptual effects, such as simultaneous contrast and color deficiencies, that make precise numerical judgments about a color scale difficult, if not impossible." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"Even if a chart is correctly designed, it may still deceive us because we don’t know how to read it correctly - we can’t grasp its symbols and grammar, so to speak - or we misinterpret its meaning, or both. Contrary to what many people believe, most good charts aren’t simple, pretty illustrations that can be understood easily and intuitively." (Alberto Cairo, "How Charts Lie", 2019)

"There is a fundamental difference between circular charts and bar charts. The brain is sensitive to angular change and (by comparison) quite numb to linear change. This is particularly true when considering motion, and sensitivity to small changes. If in your narrative, highlighting minute changes in a variable is important for the story, then circular pie charts (speed needle gauges) are the way to go. If on the contrary, too much attention to change is a distraction, avoid pie charts and needles."(Jose Berengueres & Marybeth Sandell, "Introduction to Data Visualization & Storytelling: A Guide For The Data Scientist" 2nd. Ed., 2019)

"Beyond basic charts, practitioners must also learn to compose visualizations together elegantly. The perceptual stage focuses on making the literal charts more precise as well as working to de-emphasize the entire piece. Design choices start to consider distractions, reducing visual clutter and centering on the message. Minimalism is espoused as a core value with an emphasis on shifting toward precision as accuracy. This is the most common next step for practitioners. Minimalism is also a key stage in maturation. It is experimentation at one extreme that helps practitioners distill down to core, shared practices." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"Communicating data through functionally aesthetic charts is not only about perception and precision but also understanding." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"Our visual perception is context-dependent; we are not good at seeing things in isolation." (Alan Smith, "How Charts Work: Understand and explain data with confidence", 2022)

"People feel data. They don’t just process statistics and come to rational conclusions. They form emotions about the data visualization. We are not informed by charts; we’re affected by them." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Unlike text, visual communication is governed less by an agreed-upon convention between 'writer' and 'reader' than by how our visual systems react to stimuli, often before we’re aware of it. And just as composers use music theory to create music that produces certain predictable effects on an audience, chart makers can use visual perception theory to make more-effective visualizations with similarly predictable effects." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"We see first what stands out. Our eyes go right to change and difference - peaks, valleys, intersections, dominant colors, outliers. Many successful charts - often the ones that please us the most and are shared and talked about - exploit this inclination by showing a single salient point so clearly that we feel we understand the chart’s meaning without even trying." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Your eyes and your brain always notice more dynamic visual information first and fastest. The implicit lesson is to make the idea you want people to see stand out. Conversely, make sure you’re not helping people see something that either doesn’t help convey your idea or actively fights against it." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

📉Graphical Representation: Signal (Just the Quotes)

"If statistical graphics, although born just yesterday, extends its reach every day, it is because it replaces long tables of numbers and it allows one not only to embrace at glance the series of phenomena, but also to signal the correspondences or anomalies, to find the causes, to identify the laws." (Émile Cheysson, cca. 1877)

"When large numbers of curves and charts are used by a corporation, it will be found advantageous to have certain standard abbreviations and symbols on the face of the chart so that information may be given in condensed form as a signal to anyone reading the charts." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"First, color has identity value. In other words, it serves to distinguish one thing from another. In many cases it does this much better and much quicker than black and white coding by different types of shading or lines. […] Second, color has suggestion value. […] Red is usually taken to mean a danger signal or an unfavorable condition. But since it is one of the most visible of colors it is excellent for adding emphasis, regardless of connotation. […] Green has no such unfavorable implication, and is usually appropriate for suggesting a green light" condition. […] Similarly, every color carries its own connotations; and although they seldom make a vital difference one way or the other, it seems logical to try to make them work for you rather than against you." (Kenneth W Haemer, "Color in Chart Presentation", The American Statistician Vol. 4" (2) , 1950)

"While all data contain noise, some data contain signals. Before you can detect a signal, you must filter out the noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Noise is a signal we don't like. Noise has two parts. The first has to do with the head and the second with the heart. The first part is the scientific or objective part: Noise is a signal. [...] The second part of noise is the subjective part: It deals with values. It deals with how we draw the fuzzy line between good signals and bad signals. Noise signals are the bad signals. They are the unwanted signals that mask or corrupt our preferred signals. They not only interfere but they tend to interfere at random." (Bart Kosko, "Noise", 2006)

"One person’s signal is another person’s noise and vice versa. We call this relative role reversal the noise-signal duality." (Bart Kosko, "Noise", 2006)

"A signal is a useful message that resides in data. Data that isn’t useful is noise. […] When data is expressed visually, noise can exist not only as data that doesn’t inform but also as meaningless non-data elements of the display (e.g. irrelevant attributes, such as a third dimension of depth in bars, color variation that has no significance, and artificial light and shadow effects)." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

"Data contain descriptions. Some are true, some are not. Some are useful, most are not. Skillful use of data requires that we learn to pick out the pieces that are true and useful. [...] To find signals in data, we must learn to reduce the noise - not just the noise that resides in the data, but also the noise that resides in us. It is nearly impossible for noisy minds to perceive anything but noise in data." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

"Form simplification means simplifying relationships among the components of the whole, emphasizing the whole and reducing the relevance of individual components by standardizing and generalizing relationships. This results in an increased weight of useful information (signal) against useless information (noise)." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"Before you can even consider creating a data story, you must have a meaningful insight to share. One of the essential attributes of a data story is a central or main insight. Without a main point, your data story will lack purpose, direction, and cohesion. A central insight is the unifying theme" (telos appeal) that ties your various findings together and guides your audience to a focal point or climax for your data story. However, when you have an increasing amount of data at your disposal, insights can be elusive. The noise from irrelevant and peripheral data can interfere with your ability to pinpoint the important signals hidden within its core." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

"In addition to managing how the data is visualized to reduce noise, you can also decrease the visual interference by minimizing the extraneous cognitive load. In these cases, the nonrelevant information and design elements surrounding the data can cause extraneous noise. Poor design or display decisions by the data storyteller can inadvertently interfere with the communication of the intended signal. This form of noise can occur at both a macro and micro level." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

"An outlier is a data point that is far away from other observations in your data. It may be due to random variability in the data, measurement error, or an actual anomaly. Outliers are both an opportunity and a warning. They potentially give you something very interesting to talk about, or they may signal that something is wrong in the data." (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

📉Graphical Representation: Viewers (Just the Quotes)

"Probably one of the most common misuses (intentional or otherwise) of a graph is the choice of the wrong scale - wrong, that is, from the standpoint of accurate representation of the facts. Even though not deliberate, selection of a scale that magnifies or reduces - even distorts - the appearance of a curve can mislead the viewer." (Peter H Selby, "Interpreting Graphs and Tables", 1976)

"[…] the only worse design than a pie chart is several of them, for then the viewer is asked to compare quantities located in spatial disarray both within and between pies. […] Given their low data-density and failure to order numbers along a visual dimension, pie charts should never be used." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"For many people the first word that comes to mind when they think about statistical charts is 'lie'. No doubt some graphics do distort the underlying data, making it hard for the viewer to learn the truth. But data graphics are no different from words in this regard, for any means of communication can be used to deceive. There is no reason to believe that graphics are especially vulnerable to exploitation by liars; in fact, most of us have pretty good graphical lie detectors that help us see right through frauds." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Graphical excellence is that which gives to the viewer the greatest number of ideas in the shortest time with the least ink in the smallest space." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Graphical excellence is the well-designed presentation of interesting data - a matter of substance, of statistics, and of design. Graphical excellence consists of complex ideas communicated with clarity, precision, and efficiency. Graphical excellence is that which gives to the viewer the greatest number of ideas in the shortest time with the least ink in the smallest space. Graphical excellence is nearly always multivariate. And graphical excellence requires telling the truth about the data." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"The interior decoration of graphics generates a lot of ink that does not tell the viewer anything new. The purpose of decoration varies - to make the graphic appear more scientific and precise, to enliven the display, to give the designer an opportunity to exercise artistic skills. Regardless of its cause, it is all non-data-ink or redundant data-ink, and it is often chartjunk. " (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"[…] the partial scale break is a weak indicator that the reader can fail to appreciate fully; visually the graph is still a single panel that invites the viewer to see, inappropriately, patterns between the two scales. […] The partial scale break also invites authors to connect points across the break, a poor practice indeed; […]" (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38" (4) 1984)

"The full break results in a graph with two juxtaposed panels. This use of juxtaposition to provide a full scale break, with each panel having a fill frame and its own scales, shows the scale break about as forcefully as possible and discourages mental visual connections by viewers and actual connections by authors." (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38" (4) 1984)

"Clear vision is a vital aspect of graphs. The viewer must be able to visually disentangle the many different items that appear on a graph." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Confusion and clutter are failures of design, not attributes of information. And so the point is to find design strategies that reveal detail and complexity - rather than to fault the data for an excess of complication. Or, worse, to fault viewers for a lack of understanding. Among the most powerful devices for reducing noise and enriching the content of displays is the technique of layering and separation, visually stratifying various aspects of the data." (Edward R Tufte, "Envisioning Information", 1990)

"Visual displays rich with data are not only an appropriate and proper complement to human capabilities, but also such designs are frequently optimal. If the visual task is contrast, comparison, and choice - as so often it is - then the more relevant information within eyespan, the better. Vacant, low-density displays, the dreaded posterization of data spread over pages and pages, require viewers to rely on visual memory - a weak skill - to make a contrast, a comparison, a choice." (Edward R Tufte, "Envisioning Information", 1990)

"Labels should be complete but succinct. Long and complicated labels will defeat the viewer and therefore the purpose of the graph. Treat a label as a cue to jog the memory or to complete comprehension. Shorten long labels; avoid abbreviations unless they are universally understood; avoid repetition on the same graph. A title, for instance, should not repeat what is already in the axis labels. Be consistent in terminology." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995)

"The fact that map is a fuzzy and radial, rather than a precisely defined, category is important because what a viewer interprets a display to be will influence her expectations about the display and how she interacts with it." (Alan MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"A coordinate is a number or value used to locate a point with respect to a reference point, line, or plane. Generally the reference is zero. […] The major function of coordinates is to provide a method for encoding information on charts, graphs, and maps in such a way that viewers can accurately decode the information after the graph or map has been generated. " (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"Grouped area graphs sometimes cause confusion because the viewer cannot determine whether the areas for the data series extend down to the zero axis. […] Grouped area graphs can handle negative values somewhat better than stacked area graphs but they still have the problem of all or portions of data curves being hidden by the data series towards the front." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"Data often arrive in raw form, as long lists of numbers. In this case your job is to summarize the data in a way that captures its essence and conveys its meaning. This can be done numerically, with measures such as the average and standard deviation, or graphically. At other times you find data already in summarized form; in this case you must understand what the summary is telling, and what it is not telling, and then interpret the information for your readers or viewers." (Charles Livingston & Paul Voakes, "Working with Numbers and Statistics: A handbook for journalists", 2005)

"The percentage is one of the best" (mathematical) friends a journalist can have, because it quickly puts numbers into context. And it's a context that the vast majority of readers and viewers can comprehend immediately." (Charles Livingston & Paul Voakes, "Working with Numbers and Statistics: A handbook for journalists", 2005)

"Data visualization [...] expresses the idea that it involves more than just representing data in a graphical form" (instead of using a table). The information behind the data should also be revealed in a good display; the graphic should aid readers or viewers in seeing the structure in the data. The term data visualization is related to the new field of information visualization. This includes visualization of all kinds of information, not just of data, and is closely associated with research by computer scientists." (Antony Unwin et al, "Introduction" [in "Handbook of Data Visualization"], 2008)

"When a chart is presented properly, information just lows to the viewer in the clearest and most efficient way. There are no extra layers of colors, no enhancements to distract us from the clarity of the information." (Dona Wong, "The Wall Street Journal guide to information graphics: The dos and don’ts of presenting data, facts, and figures", 2010)

"Communication is the primary goal of data visualization. Any element that hinders - rather than helps - the reader, then, needs to be changed or removed: labels and tags that are in the way, colors that confuse or simply add no value, uncomfortable scales or angles. Each element needs to serve a particular purpose toward the goal of communicating and explaining information. Efficiency matters, because if you’re wasting a viewer’s time or energy, they’re going to move on without receiving your message." (Noah Iliinsky & Julie Steel, "Designing Data Visualizations", 2011)

"A viewer’s eye must be guided to 'read' the elements in a logical order. The design of an exploratory graphic needs to allow for the additional component of discovery - guiding the viewer to first understand the overall concept and then engage her to further explore the supporting information." (Felice C Frankel & Angela H DePace, "Visual Strategies", 2012)

"A space-filling layout has the property that it fills all available space in the view, as the name implies. [...] ne advantage of space-filling approaches is that they maximize the amount of room available for color coding, increasing the chance that the colored region will be large enough to be perceptually salient to the viewer. A related advantage is that the available space representing an item is often large enough to show a label embedded within it, rather than needing more room off to the side. In contrast, one disadvantage of space-filling views is that the designer cannot make use of white space in the layout; that is, empty space where there are no explicit visual elements. Many graphic design guidelines pertain to the careful use of white space for many reasons, including readability, emphasis, relative importance, and visual balance." (Tamara Munzner, "Visualization Analysis and Design", 2014)

"Bad complexity neither elucidates important salient points nor shows coherent broader trends. It will obfuscate, frustrate, tax the mind, and ultimately convey trendlessness and confusion to the viewer. Good complexity, in contrast, emerges from visualizations that use more data than humans can reasonably process to form a few salient points." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"When the colors are dull and neutral, they can communicate a sense of uniformity and an aura of calmness. Grays do a great job of mapping out the context of your story so that the more sharp colors highlight what you’re trying to explain. The power of gray comes in handy for all of our supporting details such as the axis, gridlines, and nonessential data that is included for comparative purposes. By using gray as the primary color in a visualization, we automatically draw our viewers’ eyes to whatever isn’t gray. That way, if we are interested in telling a story about one data point, we can do so quite easily. " (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

📉Graphical Representation: Execution (Just the Quotes)

"In the course of executing that design, it occurred to me that tables are by no means a good form for conveying such information. [...] Making an appeal to the eye when proportion and magnitude are concerned is the best and readiest method of conveying a distinct idea." (William Playfair, "The Statistical Brewery", 1801)

"Simplicity, accuracy, appropriate size, proper proportion, correct emphasis, and skilled execution - these are the factors that produce the effective chart. To achieve simplicity your chart must be designed with a definite audience in mind, show only essential information. Technical terms should be absent as far as possible. And in case of doubt it is wiser to oversimplify than to make matters unduly complex. Be careful to avoid distortion or misrepresentation. Accuracy in graphics is more a matter of portraying a clear reliable picture than reiterating exact values. Selecting the right scales and employing authoritative titles and legends are as important as precision plotting. The right size of a chart depends on its probable use, its importance, and the amount of detail involved." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"The execution of any task involving information visualization will be motivated by the user's intention and influenced by many factors. One of these is the user's internal model. Another is the visible externalization of some data. A decision as to how - as well as whether - to proceed will depend upon an interpretation of these sources of information." (Robert Spence, "Information Visualization", 2001)

"Most dashboards fail to communicate efficiently and effectively, not because of inadequate technology (at least not primarily), but because of poorly designed implementations. No matter how great the technology, a dashboard's success as a medium of communication is a product of design, a result of a display that speaks clearly and immediately. Dashboards can tap into the tremendous power of visual perception to communicate, but only if those who implement them understand visual perception and apply that understanding through design principles and practices that are aligned with the way people see and think." (Stephen Few, "Information Dashboard Design", 2006)

"Good graphic design is not a panacea for bad copy, poor layout or misleading statistics. If any one of these facets are feebly executed it reflects poorly on the work overall, and this includes bad graphs and charts." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"A perfectly relevant visualization that breaks a few presentation rules is far more valuable - it’s better - than a perfectly executed, beautiful chart that contains the wrong data, communicates the wrong message, or fails to engage its audience." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Good design isn’t just choosing colors and fonts or coming up with an aesthetic for charts. That’s styling - part of design, but by no means the most important part. Rather, people with design talent develop and execute systems for effective visual communication. They understand how to create and edit visuals to focus an audience and distill ideas." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Graphic design is not just about making things look good. It is a powerful combination of form and function that uses visual elements to communicate a message. Form refers to the physical appearance of a design, such as its shape, color, and typography. Function refers to the purpose of a design, such as what it is trying to communicate or achieve. A good graphic design is both visually appealing and functional. It uses the right combination of form and function to communicate its message effectively. Graphic design is also a strategic and thoughtful craft. It requires careful planning and execution to create a design that is both effective and aesthetically pleasing." (Faith Aderemi, "The Essential Graphic Design Handbook", 2024)

📉Graphical Representation: Prototyping (Just the Quotes)

"An important rule in the drafting of curve charts is that the amount scale should begin at zero. In comparisons of size the omission of the zero base, unless clearly indicated, is likely to give a misleading impression of the relative values and trend." (Rufus R Lutz, "Graphic Presentation Simplified", 1949)

"Of course statistical graphics, just like statistical calculations, are only as good as what goes into them. An ill-specified or preposterous model or a puny data set cannot be rescued by a graphic" (or by calculation), no matter how clever or fancy. A silly theory means a silly graphic." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"The information on a plot should be relevant to the goals of the analysis. This means that in choosing graphical methods we should match the capabilities of the methods to our needs in the context of each application. [...] Scatter plots, with the views carefully selected as in draftsman's displays, casement displays, and multiwindow plots, are likely to be more informative. We must be careful, however, not to confuse what is relevant with what we expect or want to find. Often wholly unexpected phenomena constitute our most important findings." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"A good way to evaluate a model is to look at a visual representation of it. After all, what is easier to understand - a table full of mathematical relationships or a graphic displaying a decision tree with all of its splits and branches?" (Seth Paul et al. "Preparing and Mining Data with Microsoft SQL Server 2000 and Analysis", 2002)

"There are two main reasons for using graphic displays of datasets: either to present or to explore data. Presenting data involves deciding what information you want to convey and drawing a display appropriate for the content and for the intended audience. [...] Exploring data is a much more individual matter, using graphics to find information and to generate ideas.Many displays may be drawn. They can be changed at will or discarded and new versions prepared, so generally no one plot is especially important, and they all have a short life span." (Antony Unwin, "Good Graphics?" [in "Handbook of Data Visualization"], 2008)

"Although it might seem as though frittering away valuable time on sketches and models and simulations will slow work down, prototyping generates results faster." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Just as it can accelerate the pace of a project, prototyping allows the exploration of many ideas in parallel. Early prototypes should be fast, rough, and cheap. The greater the investment in an idea, the more committed one becomes to it. Overinvestment in a refined prototype has two undesirable consequences: First, a mediocre idea may go too far toward realization - or even, in the worst case, all the way. Second, the prototyping process itself creates the opportunity to discover new and better ideas at minimal cost." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"In analytics, it’s more important for individuals to be able to formulate problems well, to prototype solutions quickly, to make reasonable assumptions in the face of ill-structured problems, to design experiments that represent good investments, and to analyze results." (Foster Provost & Tom Fawcett, "Data Science for Business", 2013)

"If I had to pick a single go-to graph for categorical data, it would be the horizontal bar chart, which flips the vertical version on its side. Why? Because it is extremely easy to read. The horizontal bar chart is especially useful if your category names are long, as the text is written from left to right, as most audiences read, making your graph legible for your audience." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"The intention behind prototypes is to explore the visualization design space, as opposed to the data space. A typical project usually entails a series of prototypes; each is a tool to gather feedback from stakeholders and help explore different ways to most effectively support the higher-level questions that they have. The repeated feedback also helps validate the operationalization along the way." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"Rapid prototyping is a process of trying out many visualization ideas as quickly as possible and getting feedback from stakeholders on their efficacy. […] The design concept of 'failing fast' informs this: by exploring many different possible visual representations, it quickly becomes clear which tasks are supported by which techniques." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

📉Graphical Representation: Complexity (Just the Quotes)

"The principles of charting and curve plotting are not at all complex, and it is surprising that many business men dodge the simplest charts as though they involved higher mathematics or contained some sort of black magic. [...] The trouble at present is that there are no standards by which graphic presentations can be prepared in accordance with definite rules so that their interpretation by the reader may be both rapid and accurate. It is certain that there will evolve for methods of graphic presentation a few useful and definite rules which will correspond with the rules of grammar for the spoken and written language." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919) 

"Simplicity, accuracy, appropriate size, proper proportion, correct emphasis, and skilled execution - these are the factors that produce the effective chart. To achieve simplicity your chart must be designed with a definite audience in mind, show only essential information. Technical terms should be absent as far as possible. And in case of doubt it is wiser to oversimplify than to make matters unduly complex. Be careful to avoid distortion or misrepresentation. Accuracy in graphics is more a matter of portraying a clear reliable picture than reiterating exact values. Selecting the right scales and employing authoritative titles and legends are as important as precision plotting. The right size of a chart depends on its probable use, its importance, and the amount of detail involved." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"While circle charts are not likely to present especially new or creative ideas, they do help the user to visualize relationships. The relationships depicted by circle charts do not tend to be very complex, in contrast to those of some line graphs. Normally, the circle chart is used to portray a common type of relationship (namely. part-to-total) in an attractive manner and to expedite the message transfer from designer to user." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

"The bar or column chart is the easiest type of graphic to prepare and use in reports. It employs a simple form: four straight lines that are joined to construct a rectangle or oblong box. When the box is shown horizontally it is called a bar; when it is shown vertically it is called a column. [...] The bar chart is an effective way to show comparisons between or among two or more items. It has the added advantage of being easily understood by readers who have little or no background in statistics and who are not accustomed to reading complex tables or charts." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"The more complex the shape of any object. the more difficult it is to perceive it. The nature of thought based on the visual apprehension of objective forms suggests, therefore, the necessity to keep all graphics as simple as possible. Otherwise, their meaning will be lost or ambiguous, and the ability to convey the intended information and to persuade will be inhibited." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"Excellence in statistical graphics consists of complex ideas communicated

with clarity, precision, and efficiency. Graphical displays should

- show the data

- induce the viewer to think about the substance rather than about the

methodology, graphic design, the technology of graphic production,

or something else

- avoid distorting what the data have to say

- present many numbers in a small space

- make large data sets coherent

- encourage the eye to compare different pieces of data

- reveal the data at several levels of detail, from a broad overview to the

- serve a reasonable clear purpose: description, exploration, tabulation,

- be closely integrated." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"We can gain further insight into what makes good plots by thinking about the process of visual perception. The eye can assimilate large amounts of visual information, perceive unanticipated structure, and recognize complex patterns; however, certain kinds of patterns are more readily perceived than others. If we thoroughly understood the interaction between the brain, eye, and picture, we could organize displays to take advantage of the things that the eye and brain do best, so that the potentially most important patterns are associated with the most easily perceived visual aspects in the display." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"Confusion and clutter are failures of design, not attributes of information. And so the point is to find design strategies that reveal detail and complexity - rather than to fault the data for an excess of complication. Or, worse, to fault viewers for a lack of understanding. Among the most powerful devices for reducing noise and enriching the content of displays is the technique of layering and separation, visually stratifying various aspects of the data." (Edward R Tufte, "Envisioning Information", 1990)

"A good chart delineates and organizes information. It communicates complex ideas, procedures, and lists of facts by simplifying, grouping, and setting and marking priorities. By spatial organization, it should lead the eye through information smoothly and efficiently." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995)

"A common mistake is that all visualization must be simple, but this skips a step. You should actually design graphics that lend clarity, and that clarity can make a chart 'simple' to read. However, sometimes a dataset is complex, so the visualization must be complex. The visualization might still work if it provides useful insights that you wouldn’t get from a spreadsheet. […] Sometimes a table is better. Sometimes it’s better to show numbers instead of abstract them with shapes. Sometimes you have a lot of data, and it makes more sense to visualize a simple aggregate than it does to show every data point." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"So what is the difference between a chart or graph and a visualization? […] a chart or graph is a clean and simple atomic piece; bar charts contain a short story about the data being presented. A visualization, on the other hand, seems to contain much more ʻchart junkʼ, with many sometimes complex graphics or several layers of charts and graphs. A visualization seems to be the super-set for all sorts of data-driven design." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"The universal intelligibility of a pictogram is inversely proportional to its complexity and potential for interpretive ambiguity." (Joel Katz, "Designing Information: Human factors and common sense in information design", 2012)

"What is good visualization? It is a representation of data that helps you see what you otherwise would have been blind to if you looked only at the naked source. It enables you to see trends, patterns, and outliers that tell you about yourself and what surrounds you. The best visualization evokes that moment of bliss when seeing something for the first time, knowing that what you see has been right in front of you, just slightly hidden. Sometimes it is a simple bar graph, and other times the visualization is complex because the data requires it." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"Most of us have difficulty figuring probabilities and statistics in our heads and detecting subtle patterns in complex tables of numbers. We prefer vivid pictures, images, and stories. When making decisions, we tend to overweight such images and stories, compared to statistical information. We also tend to misunderstand or misinterpret graphics." (Daniel J Levitin, "Weaponized Lies", 2017)

"Bad complexity neither elucidates important salient points nor shows coherent broader trends. It will obfuscate, frustrate, tax the mind, and ultimately convey trendlessness and confusion to the viewer. Good complexity, in contrast, emerges from visualizations that use more data than humans can reasonably process to form a few salient points." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Confirmation is a kind of focused exploration, whereas true exploration is more open-ended. The bigger and more complex the data, and the less you know going in, the more exploratory the work. If confirmation is hiking a new trail, exploration is blazing one." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Visualization is an abstraction, a way to reduce complexity […] complexity and color catch the eye; they’re captivating. They can also make it harder to extract meaning from a chart." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"When deeply complex charts work, we find them effective and beautiful, just as we find a symphony beautiful, which is another marvelously complex arrangement of millions of data points that we experience as a coherent whole." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

📉Graphical Representation: Clusters (Just the Quotes)

"To the untrained eye, randomness appears as regularity or tendency to cluster." (William Feller, "An Introduction to Probability Theory and its Applications", 1950) 

"Sometimes clusters of variables tend to vary together in the normal course of events, thereby rendering it difficult to discover the magnitude of the independent effects of the different variables in the cluster. And yet it may be most desirable, from a practical as well as scientific point of view, to disentangle correlated describing variables in order to discover more effective policies to improve conditions. Many economic indicators tend to move together in response to underlying economic and political events." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"The logarithmic transformation serves several purposes: (1) The resulting regression coefficients sometimes have a more useful theoretical interpretation compared to a regression based on unlogged variables. (2) Badly skewed distributions - in which many of the observations are clustered together combined with a few outlying values on the scale of measurement - are transformed by taking the logarithm of the measurements so that the clustered values are spread out and the large values pulled in more toward the middle of the distribution. (3) Some of the assumptions underlying the regression model and the associated significance tests are better met when the logarithm of the measured variables is taken." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"The scatterplot is a useful exploratory method for providing a first look at bivariate data to see how they are distributed throughout the plane, for example, to see clusters of points, outliers, and so forth." (William S Cleveland, "Visualizing Data", 1993)

"The second type of uncertainty results from random causes that produce fluctuations in both sign and magnitude, the latter within well-defined limits, however. In the long run, the random error averages out to zero. The random error accounts for the variability of individual measurements and it will be shown that it can be statistically characterized by what is called a standard deviation. This term is thus a measure of the dispersion of the data around a mean or average value. When the value of the standard deviation is small, the data cluster closely around the mean; when it is large, the spread is greater." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"Because the cluster solutions grow tree-like (starting with the branches and ending with the trunk) results are often displayed in a graphic called the dendrogram. Horizontal lines indicate linking of two samples or clusters, and thus the vertical axis presents the associated height or similarity as a measure of distance. The samples are arranged in such a way that the branches of the tree do not overlap. Linking of two groups at a large height indicates strong dissimilarity (and vice versa). Therefore, a clear cluster structure would be indicated if observations are linked at a very low height, and the distinct clusters are linked at a greater height (long branches of the tree). Cutting the dendrogram at such a greater height permits assigning the samples to the resulting distinct clusters. Visual inspection of a dendrogram is often helpful in obtaining an initial estimate of the number of clusters for partitioning methods." (Clemens Reimann et al, "Statistical Data Analysis Explained: Applied Environmental Statistics with R", 2008)

"Multivariate techniques often summarize or classify many variables to only a few groups or factors (e.g., cluster analysis or multi-dimensional scaling). Parallel coordinate plots can help to investigate the influence of a single variable or a group of variables on the result of a multivariate procedure. Plotting the input variables in a parallel coordinate plot and selecting the features of interest of the multivariate procedure will show the influence of different input variables." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)

"Parallel coordinate plots are often overrated concerning their ability to depict multivariate features. Scatterplots are clearly superior in investigating the relationship between two continuous variables and multivariate outliers do not necessarily stick out in a parallel coordinate plot. Nonetheless, parallel coordinate plots can help to find and understand features such as groups/clusters, outliers and multivariate structures in their multivariate context. The key feature is the ability to select and highlight individual cases or groups in the data, and compare them to other groups or the rest of the data." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009) 

"Be careful not to confuse clustering and stratification. Even though both of these sampling strategies involve dividing the population into subgroups, both the way in which the subgroups are sampled and the optimal strategy for creating the subgroups are different. In stratified sampling, we sample from every stratum, whereas in cluster sampling, we include only selected whole clusters in the sample. Because of this difference, to increase the chance of obtaining a sample that is representative of the population, we want to create homogeneous groups for strata and heterogeneous (reflecting the variability in the population) groups for clusters." (Roxy Peck et al, "Introduction to Statistics and Data Analysis" 4th Ed., 2012)

"Hierarchical clustering creates a hierarchy of clusters which can be represented in a treelike diagram, called a dendrogram. In the dendrogram, units in the same cluster are joined by a horizontal line, with the scale on the y-axis of the dendrogram reflecting a measure of the distances of the units within the cluster. The leaves at the bottom of the dendrogram represent the individual units; leaves are combined to form small branches, small branches are combined into larger branches, until one reaches the trunk or root of the tree that represents a single cluster containing all units. Dendrograms are quite useful as they give us a visual representation of the clusters." (Johannes Ledolter, "Data mining and business analytics with R", 2013)

"Different joining/linkage rules change how the final hierarchical clustering is presented. [...] Since the barrier for merging observations and clusters is lowest with the single linkage approach, the clustering dendrogram may contain chains of clusters as well as clusters that are spread out. The barrier to joining clusters is highest with complete linkage; however, it is possible that an observation is closer to observations in other clusters than the cluster to which it has been assigned. The average linkage approach moderates the tendencies of the single or complete linkage approaches." (Glenn J Myatt & Wayne P Johnson, "Making sense of data I: a practical guide to exploratory data analysis and data mining" 2nd. Ed., 2014)

"Determining the optimal number of clusters in a data set is a fundamental issue in partitioning clustering, such as k-means clustering, which requires the user to specify the number of clusters k to be generated. Unfortunately, there is no definitive answer to this question. The optimal number of clusters is somehow subjective and depends on the method used for measuring similarities and the parameters used for partitioning. A simple and popular solution consists of inspecting the dendrogram produced using hierarchical clustering to see if it suggests a particular number of clusters. Unfortunately, this approach is also subjective." (Alboukadel Kassambara, "Practical Guide To  Cluster Analysis in R: Unsupervised Machine Learning", 2016)

"Linking is a powerful dynamic interactive graphics technique that can help us better understand high-dimensional data. This technique works in the following way: When several plots are linked, selecting an observation's point in a plot will do more than highlight the observation in the plot we are interacting with - it will also highlight points in other plots with which it is linked, giving us a more complete idea of its value across all the variables. Selecting is done interactively with a pointing device. The point selected, and corresponding points in the other linked plots, are highlighted simultaneously. Thus, we can select a cluster of points in one plot and see if it corresponds to a cluster in any other plot, enabling us to investigate the high-dimensional shape and density of the cluster of points, and permitting us to investigate the structure of the disease space." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"Hierarchical clustering is comprised of a general family of clustering algorithms that construct nested clusters by successive merging or splitting of data. The hierarchy of clusters is represented as a tree. The tree is usually called a dendrogram. The root of the dendrogram is the single cluster that contains all the samples; the leaves are the clusters containing only one sample each. This is a nice tool, since it can be straightforwardly interpreted: it 'explains' how clusters are formed and visualizes clusters at different scales. The tree that results from the technique shows the similarity between the samples. Partitioning is computed by selecting a cut on the tree at a certain level." (Laura Igual & Santi Seguí, "Introduction to Data Science: A Python Approach to Concepts, Techniques and Applications", 2017)

"Dimensionality reduction is a way of reducing a large number of different measures into a smaller set of metrics. The intent is that the reduced metrics are a simpler description of the complex space that retains most of the meaning. […] Clustering techniques are similarly useful for reducing a large number of items into a smaller set of groups. A clustering technique finds groups of items that are logically near each other and gathers them together." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"Unsupervised learning or clustering is a way of discovering hidden structures in unlabeled data. Clustering algorithms aim to discover latent patterns in unlabeled data using features to organize instances into meaningfully dissimilar groups." (Benjamin Bengfort et al, "Applied Text Analysis with Python: Enabling Language-Aware Data Products with Machine Learning", 2018)

"Important features to look for in a scatter plot are whether there is one cloud of dots or several clusters, whether there is an upward or downward slope to the cloud of dots, and whether there is any curvature to the slope." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"[...] scatterplots had advantages over earlier graphic forms: the ability to see clusters, patterns, trends, and relations in a cloud of points. Perhaps most importantly, it allowed the addition of visual annotations (point symbols, lines, curves, enclosing contours, etc.) to make those relationships more coherent and tell more nuanced stories." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

"Hierarchical clustering is summarised by a dendrogram, which sequentially shows points being joined to form a cluster, with the corresponding distances. Breaking the data into clusters is done by cutting the dendrogram at the long edges. [...] Plotting the dendrogram in the data space can help you understand how the hierarchical clustering has collected the points together into clusters. You can learn if the algorithm has been confused by nuisance patterns in the data, and how different choices of linkage method affect the result." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"Viewing the dendrograms in high dimensions provides insight into how the algorithm has joined points to clusters. For example, single linkage often has edges leading to a single focal point, which might not yield a useful clustering but might help to identify outliers. If the edges point to multiple focal points, with long edges bridging gaps in the data, the result is more likely yielding a useful clustering." (Dianne Cook & Ursula Laa,  "Interactively Exploring High-Dimensional Data and Models in R", 2026)

📉Graphical Representation: Background (Just the Quotes)

"A warning seems justifiable that the background of a chart should not be made any more prominent than actually necessary. Many charts have such heavy coordinate ruling and such relatively narrow lines for curves or other data that the real facts the chart is intended to portray do not stand out clearly from the background. No more coordinate lines should be used than are absolutely necessary to guide the eye of the reader and to permit an easy reading of the curves." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"When plotting any curve the vertical scale should, if possible, be chosen so that the zero of the scale will appear on the chart. Otherwise, the reader may assume the bottom of the chart to be zero and so be grossly misled. Zero should always be indicated by a broad line much wider than the ordinary co-ordinate lines used for the background of the chart." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"Be aware that bar charts provide ample opportunities for chart junk. The space within the bars is enticingly empty and it is tempting to put images or textures in the background. Some designers even swap out the standard bars for graphics." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"Part of the problem with using gauges and dials as alerts is that they become part of the background. If 99% of the time the needle sits in the green, the gauge isnʼt worth looking at; then that one per cent of the time when it is in the red, the gauge will go unnoticed." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"Further develop the situation or problem by covering relevant background. Incorporate external context or comparison points. Give examples that illustrate the issue. Include data that demonstrates the problem. Articulate what will happen if no action is taken or no change is made. Discuss potential options for addressing the problem. Illustrate the benefits of your recommended solution." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"In the field of design, experts speak of objects having 'affordances'. These are aspects inherent to the design that make it obvious how the product is to be used. For example, a knob affords turning, a button affords pushing, and a cord affords pulling. These characteristics suggest how the object is to be interacted with or operated. When sufficient affordances are present, good design fades into the background and you don’t even notice it." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"One thing to keep in mind with a table is that you want the design to fade into the background, letting the data take center stage. Don’t let heavy borders or shading compete for attention. Instead, think of using light borders or simply white space to set apart elements of the table." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"Visualizations can remove the background noise from enormous sets of data so that only the most important points stand out to the intended audience. This is particularly important in the era of big data. The more data there is, the more chance for noise and outliers to interfere with the core concepts of the data set." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

📉Graphical Representation: Similarity (Just the Quotes)

"Two important characteristics of maps should be noticed. A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness. If the map could be ideally correct, it would include, in a reduced scale, the map of the map; the map of the map, of the map [...]" (Alfred Korzybski, "Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics", 1933)

"Some believe that the vertical bar should be used when comparing similar items for different time periods and the horizontal bar for comparing different items for the same time period. However, most people find the vertical-bar format easier to prepare and read. and a more effective way to show most types of comparisons." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"In order to be easily understood, a display of information must have a logical structure which is appropriate for the user's knowledge and needs, and this structure must be clearly represented visually. In order to indicate structure, it is necessary to be able to eemphasiz, divide and relate items of information. Visual emphasis can be used to indicate a hierarchical relationship between items of information, as in the case of systems of headings and subheadings for example. Visual separation of items can be used to indicate that they are different in kind or are unrelated functionally, and similarly a visual relationship between items will imply that they are of a similar kind or bear some functional relation to one another. This kind of visual 'coding' helps the reader to appreciate the extent and nature of the relationship between items of information, and to adopt an appropriate scanning strategy." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"Scatter charts show the relationships between information, plotted as points on a grid. These groupings can portray general features of the source data, and are useful for showing where correlationships occur frequently. Some scatter charts connect points of equal value to produce areas within the grid which consist of similar features." (Bruce Robertson, "How to Draw Charts & Diagrams", 1988)

"Two types of graphic organizers are commonly used for comparison: the Venn diagram and the comparison matrix [...] the Venn diagram provides students with a visual display of the similarities and differences between two items. The similarities between elements are listed in the intersection between the two circles. The differences are listed in the parts of each circle that do not intersect. Ideally, a new Venn diagram should be completed for each characteristic so that students can easily see how similar and different the elements are for each characteristic used in the comparison." (Robert J. Marzano et al, "Classroom Instruction that Works: Research-based strategies for increasing student achievement, 2001)

"Arbitrary category sequence and misplaced pie chart emphasis lead to general confusion and weaken messages. Although this can be used for quite deliberate and targeted deceit, manipulation of the category axis only really comes into its own with techniques that bend the relationship between the data and the optics in a more calculated way. Many of these techniques are just twins of similar ruses on the value axis. but are none the less powerful for that." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"We tend automatically to think of all the categories represented on the horizontal axis of a column Chart as being equally important. They vary of course on the value axis. Otherwise, there would be little point in the chart, but there is somehow this feeling that they are in other respects similar members of a group. This convention can be put to good use to manipulate the message of the most boring bar or column chart." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"For a given dataset there is not a great deal of advice which can be given on content and context. Those who know their own data should know best for their specific purposes. It is advisable to think hard about what should be shown and to check with others if the graphic makes the desired impression. Design should be let to designers, though some basic guidelines should be followed: consistency is important (sets of graphics should be in similar style and use equivalent scaling); proximity is helpful (place graphics on the same page, or on the facing page, of any text that refers to them); and layout should be checked" (graphics should be neither too small nor too large and be attractively positioned relative to the whole page or display)." (Antony Unwin, "Good Graphics?" [in "Handbook of Data Visualization"], 2008)

"A histogram for discrete numerical data is a graph of the frequency or relative frequency distribution, and it is similar to the bar chart for categorical data. Each frequency or relative frequency is represented by a rectangle centered over the corresponding value" (or range of values) and the area of the rectangle is proportional to the corresponding frequency or relative frequency." (Roxy Peck et al, "Introduction to Statistics and Data Analysis" 4th Ed., 2012)

"With further similarities to small multiples, heatmaps enable us to perform rapid pattern matching to detect the order and hierarchy of different quantitative values across a matrix of categorical combinations. The use of a color scheme with decreasing saturation or increasing lightness helps create the sense of data magnitude ranking." (Andy Kirk, "Data Visualization: A successful design process", 2012)

"Tree maps are similar to pie charts in that they show parts of a whole but, unlike pie charts, they can incorporate more individual pieces without cluttering the graphic. Tree maps are particularly good at presenting information like budgets, which often include more elements than can be effectively communicated through a pie chart." (Christopher Lysy, "Developments in Quantitative Data Display and Their Implications for Evaluation", 2013)

"Upon discovering a visual image, the brain analyzes it in terms of primitive shapes and colors. Next, unity contours and connections are formed. As well, distinct variations are segmented. Finally, the mind attracts active attention to the significant things it found. That process is permanently running to react to similarities and dissimilarities in shapes, positions, rhythms, colors, and behavior. It can reveal patterns and pattern-violations among the hundreds of data values. That natural ability is the most important thing used in diagramming." (Vasily Pantyukhin, "Principles of Design Diagramming", 2015)

"A histogram represents the frequency distribution of the data. Histograms are similar to bar charts but group numbers into ranges. Also, a histogram lets you show the frequency distribution of continuous data. This helps in analyzing the distribution" (for example, normal or Gaussian), any outliers present in the data, and skewness." (Umesh R Hodeghatta & Umesha Nayak, "Business Analytics Using R: A Practical Approach", 2017)

"A taxonomy is a classification scheme that organizes categories in a broader-narrower hierarchy. Items that share similar qualities are grouped into the same category, and the taxonomy provides a global organization by relating categories to one another." (Jesús Barrasa et al, "Knowledge Graphs: Data in Context for Responsive Businesses", 2021)

"A well-designed dashboard needs to provide a similar experience; information cannot be placed just anywhere on the dashboard. Charts that relate to one another are usually positioned close to one another. Important charts often appear larger and more visually prominent than less important ones. In other words, there are natural sizes for how a dashboard comprises charts based on the task and context." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"Unlike text, visual communication is governed less by an agreed-upon convention between 'writer' and 'reader' than by how our visual systems react to stimuli, often before we’re aware of it. And just as composers use music theory to create music that produces certain predictable effects on an audience, chart makers can use visual perception theory to make more-effective visualizations with similarly predictable effects." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"The principle of similarity proposes that objects that share similar characteristics, such as color or form, tend to be perceived as a group or a pattern. Examples of data visualization techniques that account for the similarity principle in Gestalt theory include a line chart in which lines representing different categories have the same style, a bar chart in which the bar patterns or colors indicate the same group or category, and a scatterplot with different markers representing different categories of categorical variables." (Leandro N de Castro, "Exploratory Data Analysis: Descriptive Analysis, Visualization, and Dashboard Design", 2025)

See also the quotes on Similarity in Systems Engineering

📉Graphical Representation: Executives (Just the Quotes)

"An exact knowledge of conditions, and consequent timely application of praise or of constructive criticism, is one of the chief forces of the executive in securing satisfactory results. Undeserved criticism is unjust and destroys-initiative, while unmerited praise tends to render the executive ridiculous in the eyes of his subordinates; both are detrimental to discipline and weaken the power of the executive." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"The problem of the executive, then - once his organization is perfected - is to secure live data covering the exact conditions of the business at all times. These data should be arranged so as to give him all the facts, subordinated according to their relative bearing upon net earnings, and do so with the least demand upon his time. Furthermore, these facts must be so exhibited that the general laws underlying the business may be easily and accurately deduced and standards of accomplishment set which will be a continual incentive to greater accomplishment." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"Wherever unusual peaks or valleys occur on a curve it is a good plan to mark these points with a small figure inside a circle. This figure should refer to a note on the back of the chart explaining the reason for the unusual condition. It is not always sufficient to show that a certain item is unusually high or low; the executive will want to know why it is that way." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919

"An economic justification for computer graphics is that the organization spends an enormous amount of money on data processing, often providing managers with too many reports, too many data, and an overload of information. The report output has to be condensed into a more usable form. The computer graph essentially is the data represented in a structured pictorial form. The role of the graph is to provide meaningful reports. To the extent that it does. it can be justified." (Anker V Andersen, "Graphing Financial Information: How accountants can use graphs to communicate", 1983)

"Without meaningful data there can be no meaningful analysis. The interpretation of any data set must be based upon the context of those data. Unfortunately, much of the data reported to executives today are aggregated and summed over so many different operating units and processes that they cannot be said to have any context except a historical one - they were all collected during the same time period. While this may be rational with monetary figures, it can be devastating to other types of data." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Organizations face challenges of all kinds after activating their new systems. To be sure, these challenges are typically not as significant as those associated with going live. Still, executives and end users should never assume that system activation means that everyone is home free. Systems are hardly self-sufficient, and issues always appear." (Phil Simon, "Why New Systems Fail: An Insider’s Guide to Successful IT Projects", 2010)

Most discussions of decision making assume that only senior executives make decisions or that only senior executives' decisions matter. This is a dangerous mistake. Decisions are made at every level of the organization, beginning with individual professional contributors and frontline supervisors. These apparently low-level decisions are extremely important in a knowledge-based organization." (Zach Gemignani et al, "Data Fluency", 2014)

Along with the important information that executives need to be data literate, there is one other key role they play: executives drive data literacy learning and initiatives at the organization." (Jordan Morrow, "Be Data Literate: The data literacy skills everyone needs to succeed", 2021)

📉Graphical Representation: Regions (Just the Quotes)

"The most important reason for portraying standard deviations is that they give us a sense of the relative variability of the points in different regions of the plot." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"The logarithm is an extremely powerful and useful tool for graphical data presentation. One reason is that logarithms turn ratios into differences, and for many sets of data, it is natural to think in terms of ratios. […] Another reason for the power of logarithms is resolution. Data that are amounts or counts are often very skewed to the right; on graphs of such data, there are a few large values that take up most of the scale and the majority of the points are squashed into a small region of the scale with no resolution." (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38" (4) 1984)

"Do not allow data labels in the data region to interfere with the quantitative data or to clutter the graph. […] Avoid putting notes, keys, and markers in the data region. Put keys and markers just outside the data region and put notes in the legend or in the text." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Make the data stand out and avoid superfluity are two broad strategies that serve as an overall guide to the specific principles […] The data - the quantitative and qualitative information in the data region - are the reason for the existence of the graph. The data should stand out. […] We should eliminate superfluity in graphs. Unnecessary parts of a graph add to the clutter and increase the difficulty of making the necessary elements - the data - stand out." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Binning has two basic limitations. First, binning sacrifices resolution. Sometimes plots of the raw data will reveal interesting fine structure that is hidden by binning. However, advantages from binning often outweigh the disadvantage from lost resolution. [...] Second, binning does not extend well to high dimensions. With reasonable univariate resolution, say 50 regions each covering 2% of the range of the variable, the number of cells for a mere 10 variables is exceedingly large. For uniformly distributed data, it would take a huge sample size to fill a respectable fraction of the cells. The message is not so much that binning is bad but that high dimensional space is big. The complement to the curse of dimensionality is the blessing of large samples. Even in two and three dimensions having lots of data can bc very helpful when the observations are noisy and the structure non-trivial." (Daniel B Carr, "Looking at Large Data Sets Using Binned Data Plots", [in "Computing and Graphics in Statistics"] 1991)

"Data that are skewed toward large values occur commonly. Any set of positive measurements is a candidate. Nature just works like that. In fact, if data consisting of positive numbers range over several powers of ten, it is almost a guarantee that they will be skewed. Skewness creates many problems. There are visualization problems. A large fraction of the data are squashed into small regions of graphs, and visual assessment of the data degrades. There are characterization problems. Skewed distributions tend to be more complicated than symmetric ones; for example, there is no unique notion of location and the median and mean measure different aspects of the distribution. There are problems in carrying out probabilistic methods. The distribution of skewed data is not well approximated by the normal, so the many probabilistic methods based on an assumption of a normal distribution cannot be applied." (William S Cleveland, "Visualizing Data", 1993)

"A Venn diagram is a simple representation of the sample space, that is often helpful in seeing 'what is going on'. Usually the sample space is represented by a rectangle, with individual regions within the rectangle representing events. It is often helpful to imagine that the actual areas of the various regions in a Venn diagram are in proportion to the corresponding probabilities. However, there is no need to spend a long time drawing these diagrams - their use is simply as a reminder of what is happening." (Graham Upton & Ian Cook, "Introducing Statistics", 2001)

"The notion of outcomes covering a space is a very useful mental image, as it ties in strongly with the use of Venn diagrams and tables for clarifying the nature of possible events resulting from a trial. There are two important aspects to this. First, when enumerating the various outcomes that comprise an event, the number of" (equally. likely) outcomes should correspond, visually, with the area of that part of the diagram represented by the event in question - the greater the probability, the larger the area. Secondly, where events overlap" (for example, when rolling a die, consider the two events 'getting an even score' and 'getting a score greater than 2' ), the various regions in the Venn diagram help to clarify the various combinations of events that might occur." (Alan Graham, "Developing Thinking in Statistics", 2006)

"There is no strict dividing line between a region, a view, and a glyph. A view is a contiguous region in which visually encoded data is shown on the display. Sometimes a view is a full-blown window controlled by the computer’s operating system, sometimes it is a subcomponent such as a panel or a pane, and sometimes it simply means a region of the display that is visually distinguishable from other regions through some kind of visible boundary. A spatial region showing data visually encoded by a specific idiom might be called either a glyph or a view depending on its screen size, the amount of additional information beyond the visual encoding alone that is shown, and whether it is nested within another region. Large, stand-alone, highly detailed regions are likely to be called views, and small, nested, schematic regions are likely to be called glyphs." (Tamara Munzner, "Visualization Analysis and Design", 2014)

"Decision trees are also discriminative models. Decision trees are induced by recursively partitioning the feature space into regions belonging to the different classes, and consequently they define a decision boundary by aggregating the neighboring regions belonging to the same class. Decision tree model ensembles based on bagging and boosting are also discriminative models." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"When using indexes in a data set, using an average aggregation is appropriate as long as you only use it at the individual region, month, and visitor type level (i.e., the lowest granularity of the data). You cannot use an average of the average to represent the total."  (Andy Kriebel & Eva Murray, "#MakeoverMonday: Improving How We Visualize and Analyze Data, One Chart at a Time", 2018)

"Often, finding the spatial scale that best matches the task at hand is a trial-and-error procedure. It may even be necessary to create further spatial scales by subsuming or subdividing spatial units. Coarser scales can be derived from the original scale by means of a suitable aggregation strategy. This includes the application of aggregation functions such as average, sum, or count. For the creation of finer scales, a suitable distribution strategy is required to assign data values to the newly specified sub-regions. Usually, additional context information is necessary to arrive at semantically meaningful aggregations and distribution." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"Before even thinking about charts, it should be recognised that the table on its own is extremely useful. Its clear structure, with destination regions organised in columns and origins in rows, allows the reader to quickly look up any value - including totals - quickly and precisely. That’s what tables are good for. The deficiency of the table, however, is in identifying patterns within the data. Trying to understand the relationships between the numbers is difficult because, to compare the numbers with each other, the reader needs to store a lot of information in working memory, creating what psychologists refer to as a high 'cognitive load'." (Alan Smith, "How Charts Work: Understand and explain data with confidence", 2022)

📉Graphical Representation: Beauty (Just the Quotes)

"Nearly all those who produce graphics for mass publication are trained exclusively in the fine arts and have had little experience with the analysis of data. Such experiences are essential for achieving precision and grace in the presence of statistics. [...] Those who get ahead are those who beautified data, never mind statistical integrity." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Maximizing data ink (within reason) is but a single dimension of a complex and multivariate design task. The principle helps conduct experiments in graphical design. Some of those experiments will succeed. There remain, however, many other considerations in the design of statistical graphics - not only of efficiency, but also of complexity, structure, density, and even beauty." (Edward R Tufte, "Data-Ink Maximization and Graphical Design", Oikos Vol. 58 (2), 1990)

"The main goal of data visualization is its ability to visualize data, communicating information clearly and effectively. It doesn’t mean that data visualization needs to look boring to be functional or extremely sophisticated to look beautiful. To convey ideas effectively, both aesthetic form and functionality need to go hand in hand, providing insights into a rather sparse and complex dataset by communicating its key aspects in a more intuitive way. Yet designers often tend to discard the balance between design and function, creating gorgeous data visualizations which fail to serve its main purpose - communicate information." (Vitaly Friedman, "Data Visualization and Infographics", Smashing Magazine, 2008)

"A beautiful visualization has a clear goal, a message, or a particular perspective on the information that it is designed to convey. Access to this information should be as straightforward as possible, without sacrificing any necessary, relevant complexity. [...] Most importantly, beautiful visualizations reflect the qualities of the data that they represent, explicitly revealing properties and relationships inherent and implicit in the source data. As these properties and relationships become available to the reader, they bring new knowledge, insight, and enjoyment."  (Noah Iliinsky, "On Beauty", [in "Beautiful Visualization"] 2010)

"For a visual to qualify as beautiful, it must be aesthetically pleasing, yes, but it must also be novel, informative, and efficient. [...] For a visual to truly be beautiful, it must go beyond merely being a conduit for information and offer some novelty: a fresh look at the data or a format that gives readers a spark of excitement and results in a new level of understanding. Well-understood formats" (e.g., scatterplots) may be accessible and effective, but for the most part they no longer have the ability to surprise or delight us. Most often, designs that delight us do so not because they were designed to be novel, but because they were designed to be effective; their novelty is a byproduct of effectively revealing some new insight about the world." (Noah Iliinsky, "On Beauty", [in "Beautiful Visualization"] 2010)

"The first requirement of a beautiful visualization is that it is novel, fresh, or unique. It is difficult (though not impossible) to achieve the necessary novelty using default formats. In most situations, well-defined formats have well-defined, rational conventions of use: line graphs for continuous data, bar graphs for discrete data, pie graphs for when you are more interested in a pretty picture than conveying knowledge." (Noah Iliinsky, "On Beauty", [in "Beautiful Visualization"] 2010)

"The key to the success of any visual, beautiful or not, is providing access to information so that the user may gain knowledge. A visual that does not achieve this goal has failed. Because it is the most important factor in determining overall success, the ability to convey information must be the primary driver of the design of a visual." (Noah Iliinsky, "On Beauty", [in "Beautiful Visualization"] 2010)

"[...] visual art, primarily serves the relationship between the designer and the data. [...] it often entails unidirectional encoding of information, meaning that the reader may not be able to decode the visual presentation to understand the underlying information. [...] visual art merely translates the data into a visual form. The designer may intend only to condense it, translate it into a new medium, or make it beautiful; she may not intend for the reader to be able to extract anything from it other than enjoyment." (Noah Iliinsky & Julie Steel, "Designing Data Visualizations", 2011)

"Graphics, charts, and maps aren’t just tools to be seen, but to be read and scrutinized. The first goal of an infographic is not to be beautiful just for the sake of eye appeal, but, above all, to be understandable first, and beautiful after that; or to be beautiful thanks to its exquisite functionality." (Alberto Cairo, "The Functional Art", 2011)

"The biggest thing to know is that data visualization is hard. Really difficult to pull off well. It requires harmonization of several skills sets and ways of thinking: conceptual, analytic, statistical, graphic design, programmatic, interface-design, story-telling, journalism - plus a bit of ‘gut feel.’ The end result is often simple and beautiful, but the process itself is usually challenging and messy." (David McCandless, 2013)

"Aesthetics plays an important part in the process of visualization. One dimension of aesthetics is in terms of beauty, elegance and desirability. These are important attributes for the rhetorical function of visualization." (Peter A Hall & Patricio Dávila, "Critical Visualization: Rethinking the Representation of Data", 2022)

"A perfectly relevant visualization that breaks a few presentation rules is far more valuable - it’s better - than a perfectly executed, beautiful chart that contains the wrong data, communicates the wrong message, or fails to engage its audience." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"As beautiful as data can be, it’s not an al fresco painting that should be open to interpretation from anyone who walks by its section of the museum. Make bold, smart color choices that leave no doubt what the purpose of the data is." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

"When deeply complex charts work, we find them effective and beautiful, just as we find a symphony beautiful, which is another marvelously complex arrangement of millions of data points that we experience as a coherent whole." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

📉Graphical Representation: Good Design (Just the Quotes)

"Good design looks right. It is simple (clear and uncomplicated). Good design is also elegant, and does not look contrived. A map should be aesthetically pleasing, thought provoking, and communicative."  (Arthur H Robinson, "Elements of Cartography", 1953)

"Without adequate planning. it is seldom possible to achieve either proper emphasis of each component element within the chart or a presentation that is pleasing in its entirely. Too often charts are developed around a single detail without sufficient regard for the work as a whole. Good chart design requires consideration of these four major factors: (1) size, (2) proportion, (3) position and margins, and (4) composition." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"Because ease of use is the purpose, this ratio of function to conceptual complexity is the ultimate test of system design. Neither function alone nor simplicity alone defines a good design. [...] Function, and not simplicity, has always been the measure of excellence for its designers." (Fred P Brooks, "The Mythical Man-Month: Essays", 1975)

"Good design protects you from the need for too many highly accurate components in the system. But such design principles are still, to this date, ill-understood and need to be researched extensively. Not that good designers do not understand this intuitively, merely it is not easily incorporated into the design methods you were taught in school. Good minds are still needed in spite of all the computing tools we have developed." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)

"Good design, however, can dispose of clutter and show all the data points and their names. [...] Clutter calls for a design solution, not a content reduction." (Edward R Tufte, "Beautiful Evidence", 2006)

"Good design is an important part of any visualization, while decoration (or chart-junk) is best omitted. Statisticians should also be careful about comparing themselves to artists and designers; our goals are so different that we will fare poorly in comparison." (Hadley Wickham, "Graphical Criticism: Some Historical Notes", Journal of Computational and Graphical Statistics Vol. 22(1), 2013) 

"In the field of design, experts speak of objects having 'affordances'. These are aspects inherent to the design that make it obvious how the product is to be used. For example, a knob affords turning, a button affords pushing, and a cord affords pulling. These characteristics suggest how the object is to be interacted with or operated. When sufficient affordances are present, good design fades into the background and you don’t even notice it." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"For every rule in data visualization, there is a scenario where that rule should be broken. This means that choosing the best chart or the best design is always a trade-off between several conflicting goals. Our imperfect perception means that data visualization has a larger subjective dimension than a data table. Sometimes we only need this subjective, impressionist dimension and other times we need to translate it into hard figures. Striving for accuracy is important, but it’s more important to provide those insights that only a visual display can reveal." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"A chart that knows its context well will naturally end up looking better because it’s showing what it needs to show and nothing else. Good context begets good design. Good charts are only the means to a more profound end: presenting your ideas effectively. Good charts are not the product you’re after. They’re the way to deliver your product - insight." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Good design isn’t just choosing colors and fonts or coming up with an aesthetic for charts. That’s styling - part of design, but by no means the most important part. Rather, people with design talent develop and execute systems for effective visual communication. They understand how to create and edit visuals to focus an audience and distill ideas." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Good design serves a more important function than simply pleasing you: It helps you access ideas. It improves your comprehension and makes the ideas more persuasive. Good design makes lesser charts good and good charts transcendent." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Graphic design is not just about making things look good. It is a powerful combination of form and function that uses visual elements to communicate a message. Form refers to the physical appearance of a design, such as its shape, color, and typography. Function refers to the purpose of a design, such as what it is trying to communicate or achieve. A good graphic design is both visually appealing and functional. It uses the right combination of form and function to communicate its message effectively. Graphic design is also a strategic and thoughtful craft. It requires careful planning and execution to create a design that is both effective and aesthetically pleasing." (Faith Aderemi, "The Essential Graphic Design Handbook", 2024)

📉Graphical Representation: Graphs (Just the Quotes)

"Graphs are all inclusive. No fact is too slight or too great to plot to a scale suited to the eye. Graphs may record the path of an ion or the orbit of the sun, the rise of a civilization, or the acceleration of a bullet, the climate of a century or the varying pressure of a heart beat, the growth of a business, or the nerve reactions of a child." (Henry D Hubbard [foreword to Willard C Brinton, "Graphic Presentation", 1939)])

"Graphs carry the message home. A universal language, graphs convey information directly to the mind. Without complexity there is imaged to the eye a magnitude to be remembered. Words have wings, but graphs interpret. Graphs are pure quantity, stripped of verbal sham, reduced to dimension, vivid, unescapable." (Henry D Hubbard [foreword to Willard C Brinton, "Graphic Presentation", 1939]) 

"The graphic language is modern. We are learning its alphabet. That it will develop a lexicon and a literature marvelous for its vividness and the variety of application is inevitable. Graphs are dynamic, dramatic. They may epitomize an epoch, each dot a fact, each slope an event, each curve a history. Wherever there are data to record, inferences to draw, or facts to tell, graphs furnish the unrivalled means whose power we are just beginning to realize and to apply."  (Henry D Hubbard [foreword to Willard C Brinton, "Graphic Presentation", 1939)])

"A type of picture-graph less commonly used than formerly is the pictorial representation of an object which has been arbitrarily subdivided to show certain numerical relationships; as, for example, the pictorial representation of the food values of beefsteak. This is a very poor type of graphic representation, and should definitely be avoided. The irregular outline of the picture as a whole, and of each of the shaded areas, makes a comparison of the areas difficult, if not altogether impossible; the shading only to the confusion." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"Graphs showing time changes, or the increases and decreases in the amount of something over a period of time, are generally of two kinds: (1) vertical bar graphs, and (2) broken- or smooth-line graphs. Both kinds differ from the categorical charts [...] in that they have two scales instead of only one; that is why it is preferable to call them graphs rather than charts, although these terms are used rather freely and interchangeably, and there is no standard convention." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"When statistical data are of such a nature that it is permissible to assume that 'in-between values' vary continuously and uniformly (or very nearly so) from one observed or measured value to the next, a modification of the broken-line graph may be used. Instead of connecting the plotted points with straightline segments, a 'smooth' curved line is drawn between the points [...]. Such curvedline graphs may be drawn either 'free hand' or with the aid of drafting instruments known as French curves." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"You may expect to find graphs anywhere: in books, in periodicals, in newspapers, in pamphlets, on show cards in advertisements, in business reports, and so on. Their use, however, is sometimes limited. For one thing, they are of necessity less accurate than the figures on which they are based, which, of course, doesn’t matter too much in many cases. In the second place, they are sometimes misleading, which may or may not be intentional. It is also possible that the reader of a chart or graph may misinterpret it." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"If one technique of data analysis were to be exalted above all others for its ability to be revealing to the mind in connection with each of many different models, there is little doubt which one would be chosen. The simple graph has brought more information to the data analyst’s mind than any other device. It specializes in providing indications of unexpected phenomena." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics Vol. 33 (1), 1962)

"There is no more reason to expect one graph to ‘tell all’ than to expect one number to do the same." (John W Tukey, "Exploratory Data Analysis", 1977)

"[...] exploratory data analysis is an attitude, a state of flexibility, a willingness to look for those things that we believe are not there, as well as for those we believe might be there. Except for its emphasis on graphs, its tools are secondary to its purpose." (John W Tukey, [comment] 1979)

"We would wish ‘numerate’ to imply the possession of two attributes. The first of these is an ‘at-homeness’ with numbers and an ability to make use of mathematical skills which enable an individual to cope with the practical mathematical demands of his everyday life. The second is ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables or by reference to percentage increase or decrease." (Cockcroft Committee, "Mathematics Counts: A Report into the Teaching of Mathematics in Schools", 1982)

"We would wish ‘numerate’ to imply the possession of two attributes. The first of these is an ‘at-homeness’ with numbers and an ability to make use of mathematical skills which enable an individual to cope with the practical mathematical demands of his everyday life. The second is ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables or by reference to percentage increase or decrease." (Cockcroft Committee, "Mathematics Counts: A Report into the Teaching of Mathematics in Schools", 1982)

"Iteration and experimentation are important for all of data analysis, including graphical data display. In many cases when we make a graph it is immediately clear that some aspect is inadequate and we regraph the data. In many other cases we make a graph, and all is well, but we get an idea for studying the data in a different way with a different graph; one successful graph often suggests another." (William S Cleveland, "The Elements of Graphing Data", 1985)

"There are some who argue that a graph is a success only if the important information in the data can be seen within a few seconds. While there is a place for rapidly-understood graphs, it is too limiting to make speed a requirement in science and technology, where the use of graphs ranges from, detailed, in-depth data analysis to quick presentation." (William S Cleveland, "The Elements of Graphing Data", 1985)

"A first analysis of experimental results should, I believe, invariably be conducted using flexible data analytical techniques – looking at graphs and simple statistics – that so far as possible allow the data to ‘speak for themselves’. The unexpected phenomena that such a approach often uncovers can be of the greatest importance in shaping and sometimes redirecting the course of an ongoing investigation." (George Box, "Signal to Noise Ratios, Performance Criteria, and Transformations", Technometrics 30, 1988) 

"We are not saying that the primary purpose of a graph is to convey numbers with as many decimal places as possible. We agree with Ehrenberg (1975) that if this were the only goal, tables would be better. The power of a graph is its ability to enable one to take in the quantitative information, organize it, and see patterns and structure not readily revealed by other means of studying the data." (William Cleveland & Robert McGill, "Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Models", Journal of the American Statistical Association 79, 1984)

"It’s not easy to select more than a few clearly distinct colors. Also, 'distinct' is context-dependent, because: What will be the spatial relationships of the different colors in your output? You can successfully have fairly similar colors adjacent to each other, since the contrast is more obvious when they’re adjacent. However, if you want to use colors to track identity and difference across scattered points or patches, then you need bigger separations between colors, since you want to be able to see easily that patch 'A' here is of the same kind as patch 'A' there and different from patch 'B' somewhere else, when mingled with patches of other kinds. And size matters. Big patches of similar color (as on a map) can look quite distinct, while the same colors used to plot filled circular blobs on a graph might be barely distinguishable, and totally indistinguishable if used to plot colored '.'s or '+'s. [...] It’s all very psycho-visual and success usually requires experimentation!" (Ted Harding, R-help mailing list, 2004)