The Problem with Statistics

Statistics allow us to summarize data so as to convey important information about the data.
The problem, however, is that statistics aggregates data, which could lead to the loss of useful information.
Consider the Anscombe's Quartet:
The 4 scatter plots shown above represent 4 different datasets. Clearly, they have very different patterns.
However, when we compute common statistics for each of the 4 datasets, we will get the exact same results: the same average for x, the same average for y, the same linear interpolation etc. Therefore, visualization can help us see information that gets hidden by the lone use of statistics.