One of the most compelling arguments for the value of data visualization is expressed in this quote from John W Tukey (Exploratory Data Analysis).
The greatest value of a picture is when it forces us to notice what we never expected to see.
Through visualization, we are seeking to portray data in ways that allow us to see it in a new light, to visually observe patterns, exceptions, and the possible stories that sit behind its raw state. This is about considering visualization as a tool for discovery.
A well known demonstration that supports this notion was developed by noted statistician Francis Anscombe (incidentally, brother-in-law to Tukey) in the 1970s. He compiled an experiment involving four sets of data, ...