📉Graphical Representation: Skewness/Kurtosis (Just the Quotes)

"Some distributions [...] are symmetrical about their central value. Other distributions have marked asymmetry and are said to be skew. Skew distributions are divided into two types. If the 'tail' of the distribution reaches out into the larger values of the variate, the distribution is said to show positive skewness; if the tail extends towards the smaller values of the variate, the distribution is called negatively skew." (Michael J Moroney, "Facts from Figures", 1951)

"Logging size transforms the original skewed distribution into a more symmetrical one by pulling in the long right tail of the distribution toward the mean. The short left tail is, in addition, stretched. The shift toward symmetrical distribution produced by the log transform is not, of course, merely for convenience. Symmetrical distributions, especially those that resemble the normal distribution, fulfill statistical assumptions that form the basis of statistical significance testing in the regression model." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Logging skewed variables also helps to reveal the patterns in the data. […] the rescaling of the variables by taking logarithms reduces the nonlinearity in the relationship and removes much of the clutter resulting from the skewed distributions on both variables; in short, the transformation helps clarify the relationship between the two variables. It also […] leads to a theoretically meaningful regression coefficient." (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)

"It is common for positive data to be skewed to the right: some values bunch together at the low end of the scale and others trail off to the high end with increasing gaps between the values as they get higher. Such data can cause severe resolution problems on graphs, and the common remedy is to take logarithms. Indeed, it is the frequent success of this remedy that partly accounts for the large use of logarithms in graphical data display." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Visually, skewed sample distributions have one 'longer' and one 'shorter' tail. More general terms are 'heavier' and 'lighter' tails. Tail weight reflects not only distance from the center (tail length) but also the frequency of cases at that distance (tail depth, in a histogram). Tail weight corresponds to actual weight if the sample histogram were cut out of wood and balanced like a seesaw on its median (see next section). A positively skewed distribution is heavier to the right of the median; negative skew implies the opposite." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"Skewness is a measure of symmetry. For example, it's zero for the bell-shaped normal curve, which is perfectly symmetric about its mean. Kurtosis is a measure of the peakedness, or fat-tailedness, of a distribution. Thus, it measures the likelihood of extreme values." (John L Casti, "Reality Rules: Picturing the world in mathematics", 1992)

"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)

"The logarithm is one of many transformations that we can apply to univariate measurements. The square root is another. Transformation is a critical tool for visualization or for any other mode of data analysis because it can substantially simplify the structure of a set of data. For example, transformation can remove skewness toward large values, and it can remove monotone increasing spread. And often, it is the logarithm that achieves this removal." (William S Cleveland, "Visualizing Data", 1993)

"When the distributions of two or more groups of univariate data are skewed, it is common to have the spread increase monotonically with location. This behavior is monotone spread. Strictly speaking, monotone spread includes the case where the spread decreases monotonically with location, but such a decrease is much less common for raw data. Monotone spread, as with skewness, adds to the difficulty of data analysis. For example, it means that we cannot fit just location estimates to produce homogeneous residuals; we must fit spread estimates as well. Furthermore, the distributions cannot be compared by a number of standard methods of probabilistic inference that are based on an assumption of equal spreads; the standard t-test is one example. Fortunately, remedies for skewness can cure monotone spread as well." (William S Cleveland, "Visualizing Data", 1993)

"Use a logarithmic scale when it is important to under- stand percent change or multiplicative factors. […] Showing data on a logarithmic scale can cure skewness toward large values." (Naomi B Robbins, "Creating More effective Graphs", 2005)

"Before calculating a confidence interval for a mean, first check that one of the situations just described holds. To determine whether the data are bell-shaped or skewed, and to check for outliers, plot the data using a histogram, dotplot, or stemplot. A boxplot can reveal outliers and will sometimes reveal skewness, but it cannot be used to determine the shape otherwise. The sample mean and median can also be compared to each other. Differences between the mean and the median usually occur if the data are skewed - that is, are much more spread out in one direction than in the other." (Jessica M Utts & Robert F Heckard, "Mind on Statistics", 2007)

"Symmetry and skewness can be judged, but boxplots are not entirely useful for judging shape. It is not possible to use a boxplot to judge whether or not a dataset is bell-shaped, nor is it possible to judge whether or not a dataset may be bimodal." (Jessica M Utts & Robert F Heckard, "Mind on Statistics", 2007)

"Given the important role that correlation plays in structural equation modeling, we need to understand the factors that affect establishing relationships among multivariable data points. The key factors are the level of measurement, restriction of range in data values (variability, skewness, kurtosis), missing data, nonlinearity, outliers, correction for attenuation, and issues related to sampling variation, confidence intervals, effect size, significance, sample size, and power." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"While the information is of the utmost importance when it comes to soundness, what is done with the information - essentially, how it is designed - is also important. With this in mind, there are two things to consider: format and design quality. If an inappropriate format is used, the outcome will be inferior. Similarly, if the design misrepresents or skews the information deliberately or due to user error, or if the design is inappropriate given the subject matter, it cannot be considered high quality, no matter how aesthetically appealing it appears at first glance." (Jason Lankow et al, "Infographics: The power of visual storytelling", 2012)

"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)

"New information is constantly flowing in, and your brain is constantly integrating it into this statistical distribution that creates your next perception (so in this sense 'reality' is just the product of your brain’s ever-evolving database of consequence). As such, your perception is subject to a statistical phenomenon known in probability theory as kurtosis. Kurtosis in essence means that things tend to become increasingly steep in their distribution [...] that is, skewed in one direction. This applies to ways of seeing everything from current events to ourselves as we lean 'skewedly' toward one interpretation, positive or negative. Things that are highly kurtotic, or skewed, are hard to shift away from. This is another way of saying that seeing differently isn’t just conceptually difficult - it’s statistically difficult." (Beau Lotto, "Deviate: The Science of Seeing Differently", 2017)

"Many statistical procedures perform more effectively on data that are normally distributed, or at least are symmetric and not excessively kurtotic (fat-tailed), and where the mean and variance are approximately constant. Observed time series frequently require some form of transformation before they exhibit these distributional properties, for in their 'raw' form they are often asymmetric." (Terence C Mills, "Applied Time Series Analysis: A practical guide to modeling and forecasting", 2019)

"With skewed data, quantiles will reflect the skew, while adding standard deviations assumes symmetry in the distribution and can be misleading." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Skewed data means data that is shifted in one direction or the other. Skewness can cause machine learning models to underperform. Many machine learning models assume normally distributed data or data structures to follow the Gaussian structure. Any deviation from the assumed Gaussian structure, which is the popular bell curve, can affect model performance. A very effective area where we can apply feature engineering is by looking at the skewness of data and then correcting the skewness through normalization of the data." (Anthony So et al, "The Data Science Workshop" 2nd Ed., 2020)

"Adjusting scale is an important practice in data visualization. While the log transform is versatile, it doesn’t handle all situations where skew or curvature occurs. For example, at times the values are all roughly the same order of magnitude and the log transformation has little impact. Another transformation to consider is the square root transformation, which is often useful for count data." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

📉Graphical Representation: Encoding (Just the Quotes)

"The bar of a bar chart has two aspects that can be used to visually decode quantitative information-size" (length and area) and the relative position of the end of the bar along the common scale. The changing sizes of the bars is an important and imposing visual factor; thus it is important that size encode something meaningful. The sizes of bars encode the magnitudes of deviations from the baseline. If the deviations have no important interpretation, the changing sizes are wasted energy and even have the potential to mislead." (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38" (4) 1984) 

"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)

"Using area to encode quantitative information is a poor graphical method. Effects that can be readily perceived in other visualizations are often lost in an encoding by area." (William S Cleveland, "Visualizing Data", 1993)

"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) 

"[...] the form of a technological object must depend on the tasks it should help with. This is one of the most important principles to remember when dealing with infographics and visualizations: The form should be constrained by the functions of your presentation. There may be more than one form a data set can adopt so that readers can perform operations with it and extract meanings, but the data cannot adopt any form. Choosing visual shapes to encode information should not be based on aesthetics and personal tastes alone." (Alberto Cairo, "The Functional Art", 2011)

"Bear in mind is that the use of color doesn’t always help. Use it sparingly and with a specific purpose in mind. Remember that the reader’s brain is looking for patterns, and will expect both recurrence itself and the absence of expected recurrence to carry meaning. If you’re using color to differentiate categorical data, then you need to let the reader know what the categories are. If the dimension of data you’re encoding isn’t significant enough to your message to be labeled or explained in some way - or if there is no dimension to the data underlying your use of difference colors - then you should limit your use so as not to confuse the reader." (Noah Iliinsky & Julie Steel, "Designing Data Visualizations", 2011)

"By giving numbers a proper shape, by visually encoding them, the graphic has saved you time and energy that you would otherwise waste if you had to use a table that was not designed to aid your mind." (Alberto Cairo, "The Functional Art", 2011)

"To keep accuracy and efficiency of your diagrams appealing to a potential audience, explicitly describe the encoding principles we used. Titles, labels, and legends are the most common ways to define the meaning of the diagram and its elements." (Vasily Pantyukhin, "Principles of Design Diagramming", 2015)

"The first and most important functional quality of color is its suitability to the task. For example, color selection differs depending on whether you want to encode either a categorical variable or a variable with a continuous range of values. The second functional quality of color is stimuli intensity. Pure primary colors and pastel colors have different intensity levels, which allow us to establish various levels of chart reading and evaluate the stimulus intensity of each object on the chart. The final functional quality of color is, in a broad sense, its symbolism." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"We must not rush to conclude that we should always select the encoding that ensures a maximum degree of precision, which in practice would result in the exclusive use of dot charts, since those represent the example of 'position in a common scale'. "(Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"[…] no single visualization is ever quite able to show all of the important aspects of our data at once - there just are not enough visual encoding channels. […] designing effective visualizations to make sense of data is not an art - it is a systematic and repeatable process."" (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"Maps also have the disadvantage that they consume the most powerful encoding channels in the visualization toolbox - position and size - on an aspect that is held constant. This leaves less effective encoding channels like color for showing the dimension of interest." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"Too many simultaneous encodings will be overwhelming to the reader; colors must be easily distinguishable, and of a small enough number that the reader can interpret them. " (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"A map by itself requires little explanation, but once data are superimposed, readers will probably need labels on the maps, and legends explaining encodings like the color of markers." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Decision trees show the breakdown of the data by one variable then another in a very intuitive way, though they are generally just diagrams that don’t actually encode data visually." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"One very common problem in data visualization is that encoding numerical variables to area is incredibly popular, but readers can’t translate it back very well." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"[...] to support a conversation, charts need to provide cohesive and relevant responses to a user's intent. Sometimes the interface needs to respond by changing the visual encoding of existing charts, while in other cases, it is necessary to create a new chart to support the analytical conversation. In addition to appropriate visualization responses, it is critical to help the user understand how the system has interpreted their intent by producing appropriate feedback and allowing them to clarify if necessary." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"A semantic approach to visualization focuses on the interplay between charts, not just the selection of charts themselves. The approach unites the structural content of charts with the context and knowledge of those interacting with the composition. It avoids undue and excessive repetition by instead using referential devices, such as filtering or providing detail-on-demand. A cohesive analytical conversation also builds guardrails to keep users from derailing from the conversation or finding themselves lost without context. Functional aesthetics around color, sequence, style, use of space, alignment, framing, and other visual encodings can affect how users follow the script." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

Charts abstract information. They make it easier to see patterns at a distance, compare, and extrapolate. Icon encodings are graphical elements that are often used to visually represent the semantic meaning of marks for categorical data. Assigning meaningful icons to display elements helps the user perceive and interpret the visualization easier." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

📉Graphical Representation: Bad Graphics (Just the Quotes)

"The histogram, with its columns of area proportional to number, like the bar graph, is one of the most classical of statistical graphs. Its combination with a fitted bell-shaped curve has been common since the days when the Gaussian curve entered statistics. Yet as a graphical technique it really performs quite poorly. Who is there among us who can look at a histogram-fitted Gaussian combination and tell us, reliably, whether the fit is excellent, neutral, or poor? Who can tell us, when the fit is poor, of what the poorness consists? Yet these are just the sort of questions that a good graphical technique should answer at least approximately." (John W Tukey, "The Future of Processes of Data Analysis", 1965)

"The conditions under which many data graphics are produced - the lack of substantive and quantitative skills of the illustrators, dislike of quantitative evidence, and contempt for the intelligence of the audience-guarantee graphic mediocrity. These conditions engender graphics that (1) lie; (2) employ only the simplest designs, often unstandardized time-series based on a small handful of data points; and (3) miss the real news actually in the data." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Although arguments can be made that high data density does not imply that a graphic will be good, nor one with low density bad, it does reflect on the efficiency of the transmission of information. Obviously, if we hold clarity and accuracy constant, more information is better than less. One of the great assets of graphical techniques is that they can convey large amounts of information in a small space." (Howard Wainer, "How to Display Data Badly", The American Statistician Vol. 38(2), 1984)

"If the data are ordered and if the visual metaphor has a natural order, a bad display will surely emerge if you shuffle the relationship. [...] Another method is to change the meaning of the metaphor in the middle of the plot." (Howard Wainer, "How to Display Data Badly", The American Statistician Vol. 38(2), 1984)

"The aim of good data graphics is to display data accurately and clearly. Let us use this definition as a starting point for categorizing methods of bad data display. The definition has three parts. These are (a) showing data, (b) showing data accurately, and (c) showing data clearly." (Howard Wainer, "How to Display Data Badly", The American Statistician Vol. 38(2), 1984)

"The essence of a graphic display is that a set of numbers having both magnitudes and an order are represented by an appropriate visual metaphor - the magnitude and order of the metaphorical representation match the numbers. We can display data badly by ignoring or distorting this concept." (Howard Wainer, "How to Display Data Badly", The American Statistician Vol. 38(2), 1984)

"[…] 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)

"Good graphics can be spoiled by bad annotation. Labels must always be subservient to the information to be conveyed, and legibility should never be sacrificed for style. All the information on the sheet should be easy to read, and more important, easy to interpret. The priorities of the information should be clearly expressed by the use of differing sizes, weights and character of letters." (Bruce Robertson, "How to Draw Charts & Diagrams", 1988)

"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)

"Using area to encode quantitative information is a poor graphical method. Effects that can be readily perceived in other visualizations are often lost in an encoding by area." (William S Cleveland, "Visualizing Data", 1993)

"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)

"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)

"Unfortunately, setting the scale at zero is the best recipe for creating dull charts, in both senses of the word: boring and with little variation. The solution is not to break the scale, but rather to find a similar message that can be communicated using alternative metrics." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"Pitfall #1: not sharing your work with others prior to your presentation [...]
Pitfall #2: lack of audience engagement [...]
Pitfall #3: little or no eye contact with the audience [...]
Pitfall #4: making your work unreadable (small font) [...]
Pitfall #5: over the time limit [...]
Pitfall #6: showing too much information on a single slide [...]
Pitfall #7: failing to use appropriate data graphics to show insights [...]
Pitfall #8: showing a chart without an explanation [...]
Pitfall #9: presenting a chart without a clear takeaway [...]
Pitfall #10: showing so many variables on a single visual display that they impair the readability of the chart or graph" (Kristen Sosulski, "Data Visualization Made Simple: Insights into Becoming Visual", 2018)

"When there are few data points, place the data labels directly on the data. Data density refers to the amount of data shown in a visualization through encodings (points, bars, lines, etc.). A common mistake is presenting too much data in a single data graph. The data itself can obscure the insight. It can make the chart unreadable because the data values are not discernible. Examples include: overlapping data points, too many lines in a line chart, or too many slices in a pie chart. Selecting the appropriate amount of data requires a delicate balance. It is your job to determine how much detail is necessary." (Kristen Sosulski, "Data Visualization Made Simple: Insights into Becoming Visual", 2018)

📉Graphical Representation: Misinterpretation (Just the Quotes)

"Unlimited numbers of reports, magazines, and newspapers are now giving us reams of quantitative facts. If the facts were put in graphic form, not only would there be a great saving in the time of the readers but there would be infinite gain to society, because more facts could be absorbed and with less danger of misinterpretation. Graphic methods usually require no more space than is needed if the facts are presented in the form of words. In many cases, the graphic method requires less space than is required for words and there is, besides, the great advantage that with graphic methods facts are presented so that the reader may make deductions of his own, while when words are used the reader must usually accept the ready-made conclusions handed to him." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"The advantage of the pie-chart is psychological. It instantly commands the reader’s attention. A circle is, of all geometrical patterns, the easiest resting spot for the eye. The fact is well known to advertisers, who frequently use circles and circular outlines to draw attentica to their advertisements. Hence if your chart is designed for publication, or for presenta tion to readers whose attention may be easily diverted, you will find the pie-chart a powerful means for presenting your facts. Attention will be focused upon it at once, and it is as simple to understand as its name - far too simple for anyone to misunderstand. Because it is circular, there is no question but that it represents a whole and the various slices of the pie belong to their respective items."  (Karl G Karsten, "Charts and Graphs", 1925)

"Graphic charts have often been thought to be tools of those alone who are highly skilled in mathematics, but one needs to have a knowledge of only eighth-grade arithmetic to use intelligently even the logarithmic or ratio chart, which is considered so difficult by those unfamiliar with it. […] If graphic methods are to be most effective, those who are unfamiliar with charts must give some attention to their fundamental structure. Even simple charts may be misinterpreted unless they are thoroughly understood. For instance, one is not likely to read an arithmetic chart correctly unless he also appreciates the significance of a logarithmic chart." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1938)

"In line charts with an arithmetic scale, it is essential to set the base line at zero in order that the correct perspective of the general movement may not be lost. Breaking or leaving off part of the scale leads to misinterpretation, because the trend then shows a disproportionate degree of variation in movement." (Mary E Spear, "Charting Statistics", 1952)

"Although in most cases the actual value designated by a bar is determined by the location of the end of the bar, many people associate the length or area of the bar with its value. As long as the scale is linear, starts at zero, is continuous, and the bars are the same width, this presents no problem. When any of these conditions are changed, the potential exists that the graph will be misinterpreted." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"Not all statistics start out bad, but any statistic can be made worse. Numbers - even good numbers - can be misunderstood or misinterpreted. Their meanings can be stretched, twisted, distorted, or mangled. These alterations create what we can call mutant statistics - distorted versions of the original figures." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"What you design is never exactly what your audience ends up interpreting, so reducing the chances for misinterpretation becomes crucial." (Alberto Cairo, "The Functional Art", 2011)

"Readability in visualization helps people interpret data and make conclusions about what the data has to say. Embed charts in reports or surround them with text, and you can explain results in detail. However, take a visualization out of a report or disconnect it from text that provides context" (as is common when people share graphics online), and the data might lose its meaning; or worse, others might misinterpret what you tried to show." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"A common misconception is that data scientists don’t need visualizations. This attitude is not only inaccurate: it is very dangerous. Most machine learning algorithms are not inherently visual, but it is very easy to misinterpret their outputs if you look only at the numbers; there is no substitute for the human eye when it comes to making intuitive sense of things." (Field Cady, "The Data Science Handbook", 2017)

"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)

📉Graphical Representation: Heatmaps (Just the Quotes)

"Heatmaps are two-dimensional graphical representations of data where the values of a variable are shown as colors. Heatmaps are compelling for two reasons. First, the intuitive nature of the color scale as it relates to temperature minimizes the amount of learning necessary to understand it. From experience, we know that yellow is warmer than green, orange is warmer than yellow, and red is hot. It is not difficult to then figure out that the amount of heat is proportional to the level of the represented variable. Second, heatmaps show the data directly over the stimulus. Because the data could not be any closer to the elements to which they pertain, little mental effort is required to read a heatmap." (Agnieszka Bojkon, "Informative or Misleading? Heatmaps Deconstructed", [in "Human-Computer Interaction: New Trends, 13th International Conference"] 2009)

"Heat maps offer a good way to systematically identify risks, but from our point of view they have one problem - they focus on risk reduction, not risk leverage. [...] The point of the inverse heat map is to highlight opportunities that might be discarded out-of-hand because they are a gamble. If something is very unlikely (the left-hand side of the heat map), it is not worth pursuing, but opportunities that are somewhat unlikely but would have a high payoff are attractive (top right portion of the heat map)." (John W Boudreau et al, "Transformative HR: How Great Companies Use Evidence-Based Change for Sustainable Advantage", 2011)

"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)

"Heat mapping is essentially using conditional formatting, often color, to focus a reader’s attention on specific data points. Evaluators can use different colors to highlight whether output measures were met and different gradients of a single color to provide a sense of range." (Christopher Lysy, "Developments in Quantitative Data Display and Their Implications for Evaluation", 2013)

"The advantage of the calendar heat map over the line chart is that, along with seeing cycles as you scan top to bottom, it’s easy to see specific days in rows and columns, so it’s easier to reference what day of the year each value is for." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"The idiom of heatmaps is one of the simplest uses of the matrix alignment: each cell is fully occupied by an area mark encoding a single quantitative value attribute with color. […] The benefit of heatmaps is that visually encoding quantitative data with color using small area marks is very compact, so they are good for providing overviews with high information density. " (Tamara Munzner, "Visualization Analysis and Design", 2014)

"[...] a color-mapping visualization is effective if, by looking at the generated colors, we can easily and accurately make statements about the original scalar dataset that was color mapped." (Alexandru Telea, "Data Visualization: Principles and Practice" 2nd Ed., 2015)

"Compared to the rainbow colormap, the heat map uses a smaller set of hues, but adds luminance as a way to order colors in an intuitive manner. Compared to the two-hue colormap, the heat map uses more hues, thus allowing one to discriminate between more data values." (Alexandru Telea, "Data Visualization: Principles and Practice" 2nd Ed., 2015)

"Heat maps are effective visualizations for seeing concentrations as well as patterns. Adding time series to a heat map can also reveal seasonality that may not be obvious otherwise." (Andy Kriebel & Eva Murray, "#MakeoverMonday: Improving How We Visualize and Analyze Data, One Chart at a Time", 2018)

"A heatmap is a visualization where values contained in a matrix are represented as colors or color saturation. Heatmaps are great for visualizing multivariate data (data in which analysis is based on more than two variables per observation), where categorical variables are placed in the rows and columns and a numerical or categorical variable is represented as colors or color saturation." (Mario Döbler & Tim Großmann, "The Data Visualization Workshop", 2nd Ed., 2020)

"Heatmap is another representational way in which the frequencies of the various parameters of the data set is represented in different colors, much like an image captured by a thermal imaging camera in which the graph consists of varying temperatures and the temperatures are differentiated according to the colors." (Shreyans Pathak & Shashwat Pathak, "Data Visualization Techniques, Model and Taxonomy", 2020)

📉Graphical Representation: Art (Just the Quotes)

"The one thing that marks the true artist is a clear perception and a firm, bold hand, in distinction from that imperfect mental vision and uncertain truth which give up the feeble pictures and the lumpy statues of the mere artisans on canvas or in stone." (Oliver W Holmes, "The Professor at the Breakfast Table Ticknor and Fields", 1860)

"The graphic art depicts magnitudes to the eye. It does more. It compels the seeing of relations. We may portray by simple graphic methods whole masses of intricate routine, the organization of an enterprise, or the plan of a campaign. Graphs serve as storm signals for the manager, statesman, engineer; as potent narratives for the actuary, statist, naturalist; and as forceful engines of research for science, technology and industry. They display results. They disclose new facts and laws. They reveal discoveries as the bud unfolds the flower."  (Henry D Hubbard [foreword to Willard C Brinton, "Graphic Presentation", 1939)]) 

"Graphic presentation is a functional form of art as much as modern painting or architectural design. The painter studies his subject to determine what colors and style and design will best express his ideas. The same kind of imagination is exercised by the graphic artist and analyst.  In addition, the graphic analyst has some of the same problems as the architect. The modern architect studies the family, its hobbies, interests, ambitions, and financial status, among other things, before he designs the new home. The graphic analyst should make just as thorough a study of the characteristics of the data and file uses for which it is intended before he designs his project. In the same way that the architect must know his materials and how they can best be used both in traditional ways and in new ways of his own devising, so must the graphic analyst be familiar with materials and techniques." (Mary E Spear, "Charting Statistics", 1952)

"A drawing can show a true picture of both the situation as a whole and its separate components at a glance, and do the job better than could figures or the spoken word. In its essence, a chart is a medium of communication conveying a thought, an idea, a situation from one mind to another and not a work of art or a statistical table. The simpler, the more direct it is, the better it will perform that service which is its sole function." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"The art of using the language of figures correctly is not to be over-impressed by the apparent air of accuracy, and yet to be able to take account of error and inaccuracy in such a way as to know when, and when not, to use the figures. This is a matter of skill, judgment, and experience, and there are no rules and short cuts in acquiring this expertness." (Ely Devons, "Essays in Economics", 1961)

"The preparation of well-designed graphics is both an art and a skill. There are many different ways to go about the task, and readers are urged to develop their own approaches. Graphics can be creative and fun. At the same time, they require a degree of orderly and systematic work." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"Unlike some art forms. good graphics should be as concrete. geometrical, and representational as possible. A rectangle should be drawn as a rectangle, leaving nothing to the reader's imagination about what you are trying to portray. The various lines and shapes used in a graphic chart should be arranged so that it appears to be balanced. This balance is a result of the placement of shapes and lines in an orderly fashion." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"Graphical competence demands three quite different skills: the substantive, statistical, and artistic. Yet now most graphical work, particularly at news publications, is under the direction of but a single expertise-the artistic. Allowing artist-illustrators to control the design and content of statistical graphics is almost like allowing typographers to control the content, style, and editing of prose. Substantive and quantitative expertise must also participate in the design of data graphics, at least if statistical integrity and graphical sophistication are to be achieved." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Model building is the art of selecting those aspects of a process that are relevant to the question being asked. As with any art, this selection is guided by taste, elegance, and metaphor; it is a matter of induction, rather than deduction. High science depends on this art." (John H Holland, "Hidden Order: How Adaptation Builds Complexity", 1995)

"Visualization for large data is an oxymoron - the art is to reduce size before one visualizes. The contradiction (and challenge) is that we may need to visualize first in order to find out how to reduce size." (Peter Huber, "Massive datasets workshop: Four years after", Journal of Computational and Graphical Statistics Vol. 8(3), 1999)

"Models need to be judged by what they eliminate as much as by what they include - like stone carving, the art is in removing what you do not need." (John H Miller & Scott E Page, "Complex Adaptive Systems: An Introduction to Computational Models of Social Life", 2007)

"But to a ballet dancer, the art is in getting all the body parts to do those things in sync with a musical score to tell a wordless story of emotion entirely through change in position over time. In data visualization, as in physics and ballet, motion is a manifestation of the relation between time and space, and so the recording and display of motion added time as a fourth dimension to the abstract world of data." (Michael Friendly. "Milestones in the history of thematic cartography, statistical graphics, and data visualization", 2008) 

"Visual displays of empirical information are too often thought to be just compact summaries that, at their best, can clarify a muddled situation. This is partially true, as far as it goes, but it omits the magic. […] sometimes, albeit too rarely, the combination of critical questions addressed by important data and illuminated by evocative displays can achieve a transcendent, and often wholly unexpected, result. At their best, visualizations can communicate emotions and feelings in addition to cold, hard facts."  (Michael Friendly. "Milestones in the history of thematic cartography, statistical graphics, and data visualization", 2008) 

"The fact that an information graphic is designed to help us complete certain intellectual tasks is what distinguishes it from fine art." (Alberto Cairo, "The Functional Art", 2011)

"Data art is characterized by a lack of structured narrative and absence of any visual analysis capability. Instead, the motivation is much more about creating an artifact, an aesthetic representation or perhaps a technical/technique demonstration. At the extreme end, a design may be more guided by the idea of fun or playfulness or maybe the creation of ornamentation." (Andy Kirk, "Data Visualization: A successful design process", 2012)

"The art side of the field [data visualization] refers to the scope for unleashing design flair and encouraging innovation, where you strive to design communications that appeal on an aesthetic level and then survive in the mind on an emotional one." (Andy Kirk, "Data Visualization: A successful design process", 2012)

"[...] data visualization [is] a tool that, by applying perceptual mechanisms to the visual representation of abstract quantitative data, facilitates the search for relevant shapes, order, or exceptions. [...]  We must think of data visualization as a generic field where several (combinations of) perspectives, processes, technologies, and objectives (not forgetting the subjective component of personal style) can coexist. In this sense, data art, infographics, and business visualization are branches of data visualization." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"Selecting the right measure and measuring things right are both art and science. And KPIs influence management behavior as well as business culture." (Pearl Zhu, "CIO Master: Unleash the Digital Potential of It", 2016)

[…] no single visualization is ever quite able to show all of the important aspects of our data at once - there just are not enough visual encoding channels. […] designing effective visualizations to make sense of data is not an art - it is a systematic and repeatable process." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"Data visualization is part art and part science. The challenge is to get the art right without getting the science wrong and vice versa." (Claus O Wilke, "Fundamentals of Data Visualization", 2019)

"Data visualization is a mix of science and art. Sometimes we want to be closer to the science side of the spectrum - in other words, use visualizations that allow readers to more accurately perceive the absolute values of data and make comparisons. Other times we may want to be closer to the art side of the spectrum and create visuals that engage and excite the reader, even if they do not permit the most accurate comparisons." (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

📉Graphical Representation: Donut Charts (Just the Quotes)

"The donut, its spelling betrays its origins, is nearly always more deceit friendly than the pie, despite being modelled on a life-saving ring. This is because the hole destroys the second most important value- defining element, by hiding the slice angles in the middle." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"There are some chart types that occasionally appear in print but are so bad that they serve neither honesty nor deceit. Among these monuments to human ingenuity at the expense of common sense are the concentric donut and overlapping segments. The concentric donut is really just a bar or column chart bent back on itself to save space. However as anyone who has ever watched a two or four hundred metre race will know, to make sense of the order of arrival at the tape you have to stagger the start to take account of the bend in the track. Blithely ignoring this problem, the concentric donut uses to diminish the difference between the inner and the outer absolute values by anything up to 2.5 times." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"The problem is that a pie chart does one thing well, and most people don’t use it for that one thing. Specifically, they’re great at giving you a fast and accurate estimate of the part-to-whole relationship for two of the slices. Other than that, pie charts are terrible. [...] The same strengths and shortcomings that apply to the pie chart also apply to the donut chart." (Steve Wexler, "The Big Picture: How to use data visualization to make better decisions - faster", 2021)

"Donuts appear to have the advantage over pie charts of allowing for the comparison of multiple series, one in each ring, which makes them the circular version of stacked bar charts. In fact, though, there is little value in this, for it only helps to compare the first and last values of each series, just like the stacked bar chart." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"A donut chart serves the same purpose as a pie chart, built with the same parameters, with the only difference being the hole (or properly termed, the 'donut hole') in the center. [...] What purpose does the hole serve? Nothing special. We can put the total value there, but there is no such standard option. We can get this result combining two visuals: donut chart and card with total value." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI", 2024)

"[...] a sunburst chart where the center is either a pie chart or a donut chart of the biggest categories surrounded in donuts that show each of the other levels. The outside donut has the leaf nodes [...]" (Nancy Organ, "Data Visualization for People of All Ages", 2024)

"Analysis of the composition of the whole, where the emphasis is not on quantity, but on percentages. It helps to understand which segments and categories contribute the most to the overall result; for example, sales structure by markets, expenditure structure by projects. The basic figure is a circle divided into sectors. Hence the metaphor of 'pie' and 'donut'." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI: How to Design Savvy Dashboards", 2024)

"And here’s another warning - displaying the timeline at the pie or donut. It may seem like a good idea to show quarterly sales shares, and the chart will look neat. But this will distort the meaning: the timeline should be directed horizontally from left to right, from past to future. The same works for any time period: days, months, years. This is a common pattern of perception, and we do not recommend breaking it." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI: How to Design Savvy Dashboards", 2024)

"Pie and donut charts have the same purpose - visualizing the structure for a small number of categories (usually no more than six). These charts are built using the same parameters, with the only difference being that the donut chart has an inner space. They don’t have x-and yaxes, and for customization, you need to follow simple steps." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI", 2024)

"Pie charts, donut charts, and meter charts are really just stacked bar charts that have been bent - but remember that they should always add up to 100%. Radar charts use angle to show categories and position to show amounts. You can also use angle with position to create charts that show movement, direction, or change - on maps and on graphs with number axes, as well as on visualizations with category axes." (Nancy Organ, "Data Visualization for People of All Ages", 2024)

"Treemap is a visualization type used to display hierarchical data in a more structured way than pie or donut charts. In a treemap, rectangles are used instead of sectors. A treemap utilizes space more efficiently and accommodates a larger number of elements." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI", 2024)

"Structure shows which segments and categories contribute the most to the overall result. For visualizing such data, a circle divided into sectors - a pie chart - is usually used. A donut chart has the same meaning, is built on the same parameters, and differs only in the space inside." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI", 2024)

"What’s the difference between them? Studies have shown that they are perceived almost equally. Our eyes gauge the size of the outer arc: a quarter, a third, half, and so on. We surveyed our students and clients to find out which option they prefer. Some say that the ring (donut) looks somehow fresher and more interesting because the pie chart has become boring. But for others, the circle seems clearer. You can choose according to your taste. However, we prefer classic pie charts because they utilize the entire area of the figure for visualization." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI", 2024)

📉Graphical Representation: Science (Just the Quotes)

"There is no doubt that graphical expression will soon replace all others whenever one has at hand a movement or change of state - in a word, any phenomenon. Born before science, language is often inappropriate to express exact measures or definite relations." (Étienne-Jules Marey, "La méthode graphique dans les sciences expérimentales et principalement en physiologie et en médecine", 1878)

"Factual science may collect statistics, and make charts. But its predictions are, as has been well said, but past history reversed." (John Dewey, "Art as Experience", 1934)

"Experimentation with graphical methods for data presentation is important for improving graphical communication in science." (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38 (4) 1984)

"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)

"An effective dashboard is the product not of cute gauges, meters, and traffic lights, but rather of informed design: more science than art, more simplicity than dazzle. It is, above all else, about communication." (Stephen Few, "Information Dashboard Design", 2006)

"Visualization is often thought of as an exercise in graphic design or a brute-force computer science problem, but the best work is always rooted in data. To visualize data, you must understand what it is, what it represents in the real world, and in what context you should interpret it in." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"Infographics combine art and science to produce something that is not unlike a dashboard. The main difference from a dashboard is the subjective data and the narrative or story, which enhances the data-driven visual and engages the audience quickly through highlighting the required context." (Travis Murphy, "Infographics Powered by SAS®: Data Visualization Techniques for Business Reporting", 2018)

"Presenting data in a graphical format makes it much easier to see and understand what is happening with the data. Data visualization applies to all phases of the data science process."  (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"Some scientists" (e.g., econometricians) like to work with mathematical equations; others" (e.g., hard-core statisticians) prefer a list of assumptions that ostensibly summarizes the structure of the diagram. Regardless of language, the model should depict, however qualitatively, the process that generates the data - in other words, the cause-effect forces that operate in the environment and shape the data generated." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Data visualization is a mix of science and art. Sometimes we want to be closer to the science side of the spectrum - in other words, use visualizations that allow readers to more accurately perceive the absolute values of data and make comparisons. Other times we may want to be closer to the art side of the spectrum and create visuals that engage and excite the reader, even if they do not permit the most accurate comparisons." (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

"Data storytelling is a method of communicating information that is custom-fit for a specific audience and offers a compelling narrative to prove a point, highlight a trend, make a sale, or all of the above. [...] Data storytelling combines three critical components, storytelling, data science, and visualizations, to create not just a colorful chart or graph, but a work of art that carries forth a narrative complete with a beginning, middle, and end." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

"Data visualization is the practice of taking insights found in data analysis and turning them into numbers, graphs, charts, and other visual concepts to make them easier to grasp, understand, learn from, and utilize.[...] The visualization of data can be thought of as both a science and an art in that the way it is displayed is often as important to its understanding as the actual information that is being displayed." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

📉Graphical Representation: Noise (Just the Quotes)

"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)

"There are two kinds of mistakes that an inappropriate inductive bias can lead to: underfitting and overfitting. Underfitting occurs when the prediction model selected by the algorithm is too simplistic to represent the underlying relationship in the dataset between the descriptive features and the target feature. Overfitting, by contrast, occurs when the prediction model selected by the algorithm is so complex that the model fits to the dataset too closely and becomes sensitive to noise in the data." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"When we find data quality issues due to valid data during data exploration, we should note these issues in a data quality plan for potential handling later in the project. The most common issues in this regard are missing values and outliers, which are both examples of noise in the data." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 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)

"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)

"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: Indexes (Just the Quotes)

"To a very striking degree our culture has become a Statistical culture. Even a person who may never have heard of an index number is affected [...] by [...] of those index numbers which describe the cost of living. It is impossible to understand Psychology, Sociology, Economics, Finance or a Physical Science without some general idea of the meaning of an average, of variation, of concomitance, of sampling, of how to interpret charts and tables." (Carrol D Wright, 1887)

"It had appeared from observation, and it was fully confirmed by this theory, that such a thing existed as an 'Index of Correlation', that is to say, a fraction, now commonly written T, that connects with close approximation every value of the deviation on the part of the subject, with the average of all the associated deviations of the Relative [...]" (Francis Galton, "Memories of My Life", 1908)

"In any chart where index numbers are used the greatest care should be taken to select as unity a set of conditions thoroughly typical and representative. It is frequently best to take as unity the average of a series of years immediately preceding the years for which a study is to be made. The series of years averaged to represent unity should, if possible, be so selected that they will include one full cycle or wave of fluctuation. If one complete cycle involves too many years, the years selected as unity should be taken in equal number on either side of a year which represents most nearly the normal condition." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"In all chart-making, the material to be shown must be accurately compiled before it can be charted. For an understanding of the classification chart, we must delve somewhat into the mysteries of the various methods of classification and indexing. The art of classifying calls into play the power of visualizing a 'whole' together with all its 'parts'. Even in the most exact science, it is not always easy to break up a whole into a complete set of the distinct, mutually exclusive parts which together exactly compose it." (Karl G Karsten, "Charts and Graphs", 1925)

"[…] statistical literacy. That is, the ability to read diagrams and maps; a 'consumer' understanding of common statistical terms, as average, percent, dispersion, correlation, and index number."  (Douglas Scates, "Statistics: The Mathematics for Social Problems", 1943)

"The use of two or more amount scales for comparisons of series in which the units are unlike and, therefore, not comparable [...] generally results in an ineffective and confusing presentation which is difficult to understand and to interpret. Comparisons of this nature can be much more clearly shown by reducing the components to a comparable basis as percentages or index numbers." (Rufus R Lutz, "Graphic Presentation Simplified", 1949)

"It is really questionable - though bordering on heresy to put the question - whether we would be any the worse off if the whole bag of tricks were scrapped. So many of these index numbers are so ancient and so out of date, so out of touch with reality, so completely devoid of practical value when they have been computed, that their regular calculation must be regarded as a widespread compulsion neurosis. Only lunatics and public servants with no other choice go on doing silly things and liking it." (Michael J Moroney, "Facts from Figures", 1951)

"The economists, of course, have great fun - and show remarkable skill - in inventing more refined index numbers. Sometimes they use geometric averages instead of arithmetic averages (the advantage here being that the geometric average is less upset by extreme oscillations in individual items), sometimes they use the harmonic average. But these are all refinements of the basic idea of the index number [...]" (Michael J Moroney, "Facts from Figures", 1951)

"Index numbers are today one of the most widely used statistical devices…They are used to take the pulse of the economy and they have come to be used as indicators of inflationary or deflationary tendencies." (George Simpson & Fritz Kafka, "Basic Statistics", 1952)

"The great trouble with all business data upon which the statisticians and economists base their forecasts is that they are ancient history before they ever become available. They pertain to conditions which existed some weeks or months previous. The figures for what is going on at the moment in all lines of business are never available. A business index, while of great interest and value, is always historical and never predictive." (Walter E Weld, "How to Chart; Facts from Figures with Graphs", 1959)

"Every economic and social situation or problem is now described in statistical terms, and we feel that it is such statistics which give us the real basis of fact for understanding and analysing problems and difficulties, and for suggesting remedies. In the main we use such statistics or figures without any elaborate theoretical analysis; little beyond totals, simple averages and perhaps index numbers. Figures have become the language in which we describe our economy or particular parts of it, and the language in which we argue about policy." (Ely Devons, "Essays in Economics", 1961)

"The fact that index numbers attempt to measure changes of items gives rise to some knotty problems. The dispersion of a group of products increases with the passage of time, principally because some items have a long-run tendency to fall while others tend to rise. Basic changes in the demand is fundamentally responsible. The averages become less and less representative as the distance from the period increases." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"Index number is a statistical device for indicating the relative movements of the data where measurement of actual movements is difficult or incapable of being made." (Harold J Wheldon, "Business Statistics and Statistical Methods", 1968)

"The numerous design possibilities include several varieties of line graphs that are geared to particular types of problems. The design of a graph should be adapted to the type of data being structured. The data might be percentages, index numbers, frequency distributions, probability distributions, rates of change, numbers of dollars, and so on. Consequently, the designer must be prepared to structure his graph accordingly." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

"A statistical index has all the potential pitfalls of any descriptive statistic - plus the distortions introduced by combining multiple indicators into a single number. By definition, any index is going to be sensitive to how it is constructed; it will be affected both by what measures go into the index and by how each of those measures is weighted." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Once these different measures of performance are consolidated into a single number, that statistic can be used to make comparisons […] The advantage of any index is that it consolidates lots of complex information into a single number. We can then rank things that otherwise defy simple comparison […] Any index is highly sensitive to the descriptive statistics that are cobbled together to build it, and to the weight given to each of those components. As a result, indices range from useful but imperfect tools to complete charades." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Index number shows by its variations the changes in a magnitude which is not susceptible either of accurate measurement in itself or of direct valuation in practice." (Francis Y Edgeworth)

"The formula for calculating an index number should be such that it gives the same ratio between one point of comparison and the other, no matter which of the two is taken as the base or putting it another way, the index number reckoned forward should be reciprocal of the one reckoned backward." (Irving Fisher)

📉Graphical Representation: Flow Charts (Just the Quotes)

"Although flow charts are not used to portray or interpret statistical data, they possess definite utility for certain kinds of research and administrative problems. With a well-designed flow chart it is possible to present a large number of facts and relationships simply, clearly, and accurately, without resorting to extensive or involved verbal description." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"A model is a qualitative or quantitative representation of a process or endeavor that shows the effects of those factors which are significant for the purposes being considered. A model may be pictorial, descriptive, qualitative, or generally approximate in nature; or it may be mathematical and quantitative in nature and reasonably precise. It is important that effective means for modeling be understood such as analog, stochastic, procedural, scheduling, flow chart, schematic, and block diagrams." (Harold Chestnut, "Systems Engineering Tools", 1965)

"There are several classes of flowcharts used in recording study data in the Workbook. The purpose of any chart; of course, is to clarify and to make the information more understandable. One of these types of charts is a Process Flow Chart. It concerns itself with the flow of physical materials, including documents, through a system, especially in terms of distance and time. It is most useful in analyzing some of the cost and benefit factors for existing and proposed systems. System flowcharts [...] have been called the analyst's 'shorthand'. They can be forms-oriented or task-oriented. These flowcharts are not only the primary way of recording data pertinent to the current system, but are used for developing and displaying the new system as well. Later, in the implementation phase, program flowcharts, a fundamental tool of programming, would be developed." (Robert D Carlsen, "The Systems Analysis Workbook: A complete guide to project implementation and control", 1973)

"Flow charts show the decision structure of a program, which is only one aspect of its structure. They show decision structure rather elegantly when the flow chart is on one page, but the overview breaks down badly when one has multiple pages, sewed together with numbered exits and connectors." (Fred P Brooks, "The Mythical Man-Month: Essays", 1975)

"The flow chart is a most thoroughly oversold piece of program documentation. Many programs don't need flow charts at all; few programs need more than a one-page flow chart. [...] In fact, flow charting is more preached than practiced." (Fred P Brooks, "The Mythical Man-Month: Essays", 1975)

"A flow chart is a graphic method to show pictorially how a series of activities, procedures. operations. events. ideas, or other factors are related to each other. It shows the sequence, cycle. or flow of these factors and how they are connected in a series of steps from beginning to end." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"Automation is certainly one way to improve the leverage of all types of work. Having machines to help them, human beings can create more output. But in both widget manufacturing and administrative work, something else can also increase the productivity of the black box. This is called work simplification. To get leverage this way, you first need to create a flow chart of the production process as it exists. Every single step must be shown on it; no step should be omitted in order to pretty things up on paper. Second, count the number of steps in the flow chart so that you know how many you started with. Third, set a rough target for reduction of the number of steps." (Andrew S Grove, "High Output Management", 1983)

"System dynamics [...] uses models and computer simulations to understand behavior of an entire system, and has been applied to the behavior of large and complex national issues. It portrays the relationships in systems as feedback loops, lags, and other descriptors to explain dynamics, that is, how a system behaves over time. Its quantitative methodology relies on what are called 'stock-and-flow diagrams' that reflect how levels of specific elements accumulate over time and the rate at which they change. Qualitative systems thinking constructs evolved from this quantitative discipline." (Karen L Higgins, "Economic Growth and Sustainability: Systems Thinking for a Complex World", 2015)

📉Graphical Representation: Tree Maps (Just the Quotes)

"The great advantage of the treemap over conventional tree views is that the amount of information on each branch of the tree can be easily visualized. Because the method is space-filling, it can show quite large trees containing thousands of branches. The disadvantage is that the hierarchical structure is not as clear as it is in a more conventional tree drawing, which is a specialized form of node–link diagram." (Colin Ware, "Information Visualization: Perception for Design" 2nd Ed., 2004)

"Like a pie chart, a treemap is used for a part-of-a-whole analysis, but because you have better control over the rectangle sizes than over slices, you can have many more data points. Unlike with traditional pie charts, you can arrange the data hierarchically. You can compare a rectangle to all data points or to its own branch." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"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)

"Even though its recursive composition is similar to rectangular treemaps, the Voronoi treemap allows an improved sub division of a given area that avoids similar shapes and aspect ratios, by making the location and contour of individual cells highly adaptive and configurable. Due to their flexible organizational principle, Voronoi treemaps are known for their organic layouts, featuring a rich, diverse assortment of shapes and con figurations that can resemble stained glass or enthralling natural patterns. The model has wide applicability and it has proved popular in the visualization of file systems and genome data." (Manuel Lima, "The Book of Trees: Visualizing Branches of Knowledge", 2014)

"Of all visualization models, vertical trees are the ones that retain the strongest resemblance to figurative trees, due to their vertical layout and forking arrangement from a central trunk. In most cases they are inverted trees, with the root at the top, emphasizing the notion of descent and representing a more natural writing pattern from top to bottom." (Manuel Lima, "The Book of Trees: Visualizing Branches of Knowledge", 2014)

"Sunbursts, also known as radial treemaps, tree rings, fan charts, or nested pie charts, are a space-filling visualization technique that uses a radial layout, as opposed to the more widespread rectangular type. Similar to radial trees, sunbursts normally start with a central root, or top level of hierarchy, with the remaining ranks expanding outward from the middle. However, instead of a node-link construct sunbursts employ a sequence of segmented rings and juxtaposed cells" (Manuel Lima, "The Book of Trees: Visualizing Branches of Knowledge", 2014)

"The rectangular treemap, sometimes called the mosaic graph, is a space-filling visualization model used for displaying hierarchical data by means of nested rectangles. Each major branch of the tree is depicted as a rectangle, which is then sequentially tiled with smaller rectangles representing its subbranches. The area of each individual cell generally corresponds to a given quantity or data attri bute, for example size, length, price, time, or temperature. Color can indicate an additional quality, such as type, class, gender, or category." (Manuel Lima, "The Book of Trees: Visualizing Branches of Knowledge", 2014)

"The decomposition tree is an interactive visualization for hierarchical data. The concept is to take a single metric and drill it down into various dimensions." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI", 2024)

"Treemap is a visualization type used to display hierarchical data in a more structured way than pie or donut charts. In a treemap, rectangles are used instead of sectors. A treemap utilizes space more efficiently and accommodates a larger number of elements." (Alex Kolokolov & Maxim Zelensky, "Data Visualization with Microsoft Power BI", 2024)

📉Graphical Representation: Phenomena (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)

"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)

"Information needs representation. The idea that it is possible to communicate information in a 'pure' form is fiction. Successful risk communication requires intuitively clear representations. Playing with representations can help us not only to understand numbers (describe phenomena) but also to draw conclusions from numbers" (make inferences). There is no single best representation, because what is needed always depends on the minds that are doing the communicating." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"[…] a graph is nothing but a visual metaphor. To be truthful, it must correspond closely to the phenomena it depicts: longer bars or bigger pie slices must correspond to more, a rising line must correspond to an increasing amount. If a graphical depiction of data does not faithfully follow this principle, it is almost sure to be misleading. But the metaphoric attachment of a graphic goes farther than this. The character of the depiction ism a necessary and sufficient condition for the character of the data. When the data change, so too must their depiction; but when the depiction changes very little, we assume that the data, likewise, are relatively unchanging. If this convention is not followed, we are usually misled." (Howard Wainer, "Graphic Discovery: A trout in the milk and other visuals" 2nd, 2008)

"Nothing that had been produced before was even close. Even today, after more than two centuries of graphical experience, Playfair’s graphs remain exemplary standards for clearcommunication of quantitative phenomena. […] Graphical forms were available before Playfair, but they were rarely used to plot empirical information." (Howard Wainer, "Graphic Discovery: A trout in the milk and other visuals" 2nd, 2008)

"Oftentimes a statistical graphic provides the evidence for a plausible story, and the evidence, though perhaps only circumstantial, can be quite convincing. […] But such graphical arguments are not always valid. Knowledge of the underlying phenomena and additional facts may be required." (Howard Wainer, "Graphic Discovery: A trout in the milk and other visuals" 2nd, 2008)

"[...] graphical displays can be either figurative or non-figurative.[…] Other graphics that display abstract phenomena are non-figurative. In these ,there is no mimetic correspondence between what is being represented and its representation. The relationship between those two entities is conventional, no tnatural [...]." (Alberto Cairo, "The Functional Art", 2011)

"[...] without conscious effort, the brain always tries to close the distance between observed phenomena and knowledge or wisdom that can help us survive. This is what cognition means. The role of an information architect is to anticipate this process and generate order before people’s brains try to do it on their own." (Alberto Cairo, "The Functional Art", 2011)

"Correlation measures the degree to which two phenomena are related to one another. [...] Two variables are positively correlated if a change in one is associated with a change in the other in the same direction, such as the relationship between height and weight. [...] A correlation is negative if a positive change in one variable is associated with a negative change in the other, such as the relationship between exercise and weight." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"The first epistemic principle to embrace is that there is always a gap between our data and the real world. We fall headfirst into a pitfall when we forget that this gap exists, that our data isn't a perfect reflection of the real-world phenomena it's representing. Do people really fail to remember this? It sounds so basic. How could anyone fall into such an obvious trap?" (Ben Jones, "Avoiding Data Pitfalls: How to Steer Clear of Common Blunders When Working with Data and Presenting Analysis and Visualizations", 2020)

"Data visualizations also gain power through how they juxtapose different data sets to draw out a relationship between different phenomena." (Peter A Hall & Patricio Dávila, "Critical Visualization: Rethinking the Representation of Data", 2022)

📉Graphical Representation: Axes (Just the Quotes)

"A type of chart which has received considerable attention of late years and which differs radically from those 'already described is that known as the alinement chart. In the charts hitherto examined the necessary lines were plotted on what are known as rectangular coordinates; that is, the axes on which the values of x and y were plotted met at a right angle. This is by no means a necessary condition. The axes may be parallel [...]" (John B Peddle, "The Construction of Graphical Charts", 1910)

"The graduated lengths along the different axes may be anything we choose to make them. In general, they should be about equal and as long as possible while keeping the size of the chart within reasonable limits." (John B Peddle, "The Construction of Graphical Charts", 1910)

"When an alinement chart is intended to cover a considerable range of values we are confronted with the difficulty that it must be large, and therefore awkward to handle, or we must have scale divisions which are too small for accurate reading. These difficulties may be overcome with but little additional trouble by a system of double graduation of the axes." (John B Peddle, "The Construction of Graphical Charts", 1910)

"Another principle which will quickly appeal to your common sense, is the rule that when zero is real, the zero-line should be extra heavy to make it prominent. Remember that it takes the place of the floor or lower end of the bars in the bar-chart. It should stand out, therefore, in such a way that the reader can easily grasp its significance and compare with it the heights of the points on the curve. The rule is particularly important in cases where the chart extends down below the zero line into the negative side in order to show negative and positive values. On the same principle the 100% line, when it occurs in a chart, should be similarly heavy as it also may be considered a base for zero points, being the point of zero loss or gain. In fact, the rule may be extended to all cases of lines showing significant constant values, and the zero line should not be heavy, unless it has a special significance." (Karl G Karsten, "Charts and Graphs", 1925)

"In short, the rule that no more dimensions or axes should be used in the chart than the data calls for, is fundamental. Violate this rule and you bring down upon your head a host of penalties. In the first place, you complicate your computing processes, or else achieve a grossly deceptive chart. If your chart becomes deceptive, it has defeated its purpose, which was to represent accurately. Unless, of course, you intended to deceive, in which case we are through with you and leave you to Mark Twain’s mercies. If you make your chart accurate, at the cost of considerable square or cube root calculating, you still have no hope, for the chart is not clear; your reader is more than likely to misunderstand it. Confusion, inaccuracy and deception always lie in wait for you down the path departing from the principle we have discussed - and one of them is sure to catch you." (Karl G Karsten, "Charts and Graphs", 1925)

"The ratio chart not only correctly represents relative changes but also indicates absolute amounts at the same time. Because of its distinctive structure, it is referred to as a semilogarithmic chart. The vertical axis is ruled logarithmically and the horizontal axis arithmetically. The continued narrowing of the spacings of the scale divisions on the vertical axis is characteristic of logarithmic rulings; the equal intervals on the horizontal axis are indicative of arithmetic rulings." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"As a general rule, plotted points and graph lines should be given more 'weight' than the axes. In this way the 'meat' will be easily distinguishable from the 'bones'. Furthermore, an illustration composed of lines of unequal weights is always more attractive than one in which all the lines are of uniform thickness. It may not always be possible to emphasise the data in this way however. In a scattergram, for example, the more plotted points there are, the smaller they may need to be and this will give them a lighter appearance. Similarly, the more curves there are on a graph, the thinner the lines may need to be. In both cases, the axes may look better if they are drawn with a somewhat bolder line so that they are easily distinguishable from the data." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"The frequency of labelled scale calibrations on the axes of a graph can significantly affect the accuracy with which it is interpreted. As little interpolation as possible should be required of the user, in order to minimise errors. If single units cannot be marked, it has been suggested that multiples of 2,5 or 10 should be used." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"The plotted points on a graph should always be made to stand out well. They are, after all, the most important feature of a graph, since any lines linking them are nearly always a matter of conjecture. These lines should stop just short of the plotted points so that the latter are emphasised by the space surrounding them. Where a point happens to fall on an axis line, the axis should be broken for a short distance on either side of the point." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"At a simpler level, some elementary but important suggestions for the clarity of graphs are as follows: (i) the axes should be clearly labelled with the names of the variables and the units of measurement; (ii) scale breaks should be used for false origins; (iii) comparison of related diagrams should be made easy, for example by using identical scales of measurement and placing diagrams side by side; (iv) scales should be arranged so that systematic and approximately linear relations are plotted at roughly 45° to the x-axis; (v) legends should make diagrams as nearly self-explanatory, i.e. independent of the text, as is feasible; (vi) interpretation should not be prejudiced by the technique of presentation, for example by superimposing thick smooth curves on scatter diagrams of points faintly reproduced." (David R Cox,"Some Remarks on the Role in Statistics of Graphical Methods", Applied Statistics 27 (1), 1978) 

"Most graphs used in the analysis of data consist of points arising in effect from distinct individuals, although there are certainly other possibilities, such as the use of lines dual to points. In many cases of exploratory analysis, however, the display of supplementary information attached to some or all of the points will be crucial for successful interpretation. The primary co-ordinate axes should, of course, be chosen to express the main dependence explicitly, if not initially certainly in the final presentation of conclusions." David R Cox,"Some Remarks on the Role in Statistics of Graphical Methods", Applied Statistics 27 (1), 1978)

"An axis is the ruler that establishes regular intervals for measuring information. Because it is such a widely accepted convention, it is often taken for granted and its importance overlooked. Axes may emphasize, diminish, distort, simplify, or clutter the information. They must be used carefully and accurately." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995)

"Graphic misrepresentation is a frequent misuse in presentations to the nonprofessional. The granddaddy of all graphical offenses is to omit the zero on the vertical axis. As a consequence, the chart is often interpreted as if its bottom axis were zero, even though it may be far removed. This can lead to attention-getting headlines about 'a soar' or 'a dramatic rise (or fall)'. A modest, and possibly insignificant, change is amplified into a disastrous or inspirational trend." (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)

"If you want to show the growth of numbers which tend to grow by percentages, plot them on a logarithmic vertical scale. When plotted against a logarithmic vertical axis, equal percentage changes take up equal distances on the vertical axis. Thus, a constant annual percentage rate of change will plot as a straight line. The vertical scale on a logarithmic chart does not start at zero, as it shows the ratio of values (in this case, land values), and dividing by zero is impossible." (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)

"The visual representation of a scale - an axis with ticks - looks like a ladder. Scales are the types of functions we use to map varsets to dimensions. At first glance, it would seem that constructing a scale is simply a matter of selecting a range for our numbers and intervals to mark ticks. There is more involved, however. Scales measure the contents of a frame. They determine how we perceive the size, shape, and location of graphics. Choosing a scale (even a default decimal interval scale) requires us to think about what we are measuring and the meaning of our measurements. Ultimately, that choice determines how we interpret a graphic." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"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)

"One of the easiest ways to display data badly is to display as little information as possible. This includes not labelling axes and titles adequately, and not giving units. In addition, information that is displayed can be obscured by including unnecessary and distracting details." (Jenny Freeman et al, "How to Display Data", 2008)

"Histograms are often mistaken for bar charts but there are important differences. Histograms show distribution through the frequency of quantitative values (y axis) against defined intervals of quantitative values (x axis). By contrast, bar charts facilitate comparison of categorical values. One of the distinguishing features of a histogram is the lack of gaps between the bars [...]" (Andy Kirk, "Data Visualization: A successful design process", 2012)

"Because we should, whenever possible, try to understand relationships between variables and not only describe each one of them in isolation, scatter plots are the most powerful charts available to us. The connected scatter plot is not easy to read at first, but I strongly encourage you to become familiar with it - at least during the exploratory stage - to check for relevant shapes in the relationships. Whenever you feel the need to use a dual-axis chart with two independent variables, you should try the connected scatter plot first." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"The use of dual-axis charts is a subtle form of graphical lie through which [...] a spurious relationship is established between variables. Considering that the author of a dual-axis chart tries to harmonize the representation, it’s natural to break some rules: The vertical scale is one of the first victims." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

📉Graphical Representation: Aggregation (Just the Quotes)

"Modern data graphics can do much more than simply substitute for small statistical tables. At their best, graphics are instruments for reasoning about quantitative information. Often the most effective way to describe, explore, and summarize a set of numbers even a very large set - is to look at pictures of those numbers. Furthermore, of all methods for analyzing and communicating statistical information, well-designed data graphics are usually the simplest and at the same time the most powerful." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"A good description of the data summarizes the systematic variation and leaves residuals that look structureless. That is, the residuals exhibit no patterns and have no exceptionally large values, or outliers. Any structure present in the residuals indicates an inadequate fit. Looking at the residuals laid out in an overlay helps to spot patterns and outliers and to associate them with their source in the data." (Christopher H Schrnid, "Value Splitting: Taking the Data Apart", 1991)

"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)

"Graphical displays are often constructed to place principal focus on the individual observations in a dataset, and this is particularly helpful in identifying both the typical positions of data points and unusual or influential cases. However, in many investigations, principal interest lies in identifying the nature of underlying trends and relationships between variables, and so it is often helpful to enhance graphical displays in ways which give deeper insight into these features. This can be very beneficial both for small datasets, where variation can obscure underlying patterns, and large datasets, where the volume of data is so large that effective representation inevitably involves suitable summaries." (Adrian W Bowman, "Smoothing Techniques for Visualisation" [in "Handbook of Data Visualization"], 2008)

"In order to be effective a descriptive statistic has to make sense - it has to distill some essential characteristic of the data into a value that is both appropriate and understandable. […] the justification for computing any given statistic must come from the nature of the data themselves - it cannot come from the arithmetic, nor can it come from the statistic. If the data are a meaningless collection of values, then the summary statistics will also be meaningless - no arithmetic operation can magically create meaning out of nonsense. Therefore, the meaning of any statistic has to come from the context for the data, while the appropriateness of any statistic will depend upon the use we intend to make of that statistic." (Donald J Wheeler, "Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

"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)

"A boxplot is a dotplot enhanced with a schematic that provides information about the center and spread of the data, including the median, quartiles, and so on. This is a very useful way of summarizing a variable's distribution. The dotplot can also be enhanced with a diamond-shaped schematic portraying the mean and standard deviation (or the standard error of the mean)." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"Just as with aggregated data, an average is a summary statistic that can tell you something about the data - but it is only one metric, and oftentimes a deceiving one at that. By taking all of the data and boiling it down to one value, an average (and other summary statistics) may imply that all of the underlying data is the same, even when it’s not." (John H Johnson & Mike Gluck, "Everydata: The misinformation hidden in the little data you consume every day", 2016)

"Dashboards are a type of multiform visualization used to summarize and monitor data. These are most useful when proxies have been well validated and the task is well understood. This design pattern brings a number of carefully selected attributes together for fast, and often continuous, monitoring - dashboards are often linked to updating data streams. While many allow interactivity for further investigation, they typically do not depend on it. Dashboards are often used for presenting and monitoring data and are typically designed for at-a-glance analysis rather than deep exploration and analysis." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"A data visualization, or dashboard, is great for summarizing or describing what has gone on in the past, but if people don’t know how to progress beyond looking just backwards on what has happened, then they cannot diagnose and find the ‘why’ behind it." (Jordan Morrow, "Be Data Literate: The data literacy skills everyone needs to succeed", 2021)

"Visual displays of empirical information are too often thought to be just compact summaries that, at their best, can clarify a muddled situation. This is partially true, as far as it goes, but it omits the magic. […] sometimes, albeit too rarely, the combination of critical questions addressed by important data and illuminated by evocative displays can achieve a transcendent, and often wholly unexpected, result. At their best, visualizations can communicate emotions and feelings in addition to cold, hard facts." (Michael Friendly. "Milestones in the history of thematic cartography, statistical graphics, and data visualization", 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)

"Smoothing and aggregating can help us see important features and relationships, but when we have only a handful of observations, smoothing techniques can be misleading. With just a few observations, we prefer rug plots over histograms, box plots, and density curves, and we use scatterplots rather than smooth curves and density contours. This may seem obvious, but when we have a large amount of data, the amount of data in a subgroup can quickly dwindle. This phenomenon is an example of the curse of dimensionality." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

"Visualisation is fundamentally limited by the number of pixels you can pump to a screen. If you have big data, you have way more data than pixels, so you have to summarise your data. Statistics gives you lots of really good tools for this." (Hadley Wickham)