#### Overview of this book

Mathematica Data Visualization
Credits
www.PacktPub.com
Preface
Free Chapter
Visualization as a Tool to Understand Data
Dissecting Data Using Mathematica
Time Series and Scientific Visualization
Statistical and Information Visualization
Maps and Aesthetics
Index

## The importance of visualization

Visualization has a broad definition, and so does data. The cave paintings drawn by our ancestors can be argued as visualizations as they convey historical data through a visual medium. Map visualizations were commonly used in wars since ancient times to discuss the past, present, and future states of a war, and to come up with new strategies. Astronomers in the 17th century were believed to have built the first visualization of their statistical data. In the 18th century, William Playfair invented many of the popular graphs we use today (line, bar, circle, and pie charts). Therefore, it appears as if many, since ancient times, have recognized the importance of visualization in giving some meaning to data.

To demonstrate the importance of visualization in a simple mathematical setting, consider fitting a line to a given set of points. Without looking at the data points, it would be unwise to try to fit them with a model that seemingly lowers the error bound. It should also be noted that sometimes, the data needs to be changed or transformed to the correct form that allows us to use a particular tool. Visualizing the data points ensures that we do not fall into any trap. The following screenshot shows the visualization of a polynomial as a circle:

Figure 1.1 Fitting a polynomial

In figure 1.1, the points are distributed around a circle. Imagine we are given these points in a Cartesian space (orthogonal x and y coordinates), and we are asked to fit a simple linear model. There is not much benefit if we try to fit these points to any polynomial in a Cartesian space; what we really need to do is change the parameter space to polar coordinates. A 1-degree polynomial in polar coordinate space (essentially a circle) would nicely fit these points when they are converted to polar coordinates, as shown in figure 1.1. Visualizing the data points in more complicated but similar situations can save us a lot of trouble. The following is a screenshot of Anscombe's quartet:

Figure 1.2 Anscombe's quartet, generated using Mathematica