01 August 2026

🧊On Geometry: On Curves (2020-2029)

"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)

"Correlation does not imply causation: often some other missing third variable is influencing both of the variables you are correlating. […] The need for a scatterplot arose when scientists had to examine bivariate relations between distinct variables directly. As opposed to other graphic forms - pie charts, line graphs, and bar charts - the scatterplot offered a unique advantage: the possibility to discover regularity in empirical data (shown as points) by adding smoothed lines or curves designed to pass 'not through, but among them', so as to pass from raw data to a theory-based description, analysis, and understanding." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

"Standard graphs, like bar and line charts, are so common because they are perceptually more accurate, familiar to people, and easy to create. Nonstandard graphs - those that use circles or curves, for instance - may not allow the reader to most accurately perceive the exact data values. But perceptual accuracy is not always the goal. And sometimes it's not a goal at all. Spurring readers to engage with a graph is sometimes just as important. Sometimes, it's more important. And nonstandard chart types may do just that. In some cases, nonstandard graphs may help show underlying patterns and trends in better ways that standard graphs. In other cases, the fact that these nonstandard graphs are different may make them more engaging, which we may sometimes need to first attract attention to the visualization."  (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

"Ignoring sampling weights can give a misleading presentation of a distribution. Whether for a histogram, bar plot, box plot, two-dimensional contour, or smooth curve, we need to use the weights to get a representative plot." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

"Side-by-side box plots offer a similar comparison of distributions across groups. The box plot offers a simpler approach that can give a crude understanding of a distribution. Likewise, violin plots sketch density curves along an axis for each group. The curve is flipped to create a symmetric 'violin' shape. The violin plot aims to bridge the gap between the density curve and box plot." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

"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)

"Stacked line plots are even more difficult to read because we have to judge the gap between curves as they jiggle up and down." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

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🧊On Geometry: On Curves (2020-2029)

"Skewed data means data that is shifted in one direction or the other. Skewness can cause machine learning models to underperform. Many...