In an earlier image, we saw three very different distributions, all with the same mean and median. I said then that we need to quantify variance to tell them apart. In the following image, there are three very different distributions, all with the same mean, median, and variance:
Figure 2.10: Three PDFs with the same mean, median, and standard deviation
If you just rely on basic summary statistics to understand univariate data, you'll never get the full picture. It's only when we visualize it that we can clearly see, at a glance, whether there are any clusters or areas with a high density of data points, the number of clusters there are, whether there are outliers, whether there is a pattern to the outliers, and so on. When dealing with univariate data, the shape is the most important part. (That's why this chapter is called Shape of Data!)
We will be using ggplot2's qplot
function to investigate these shapes and visualize this data. qplot
(for quick plot) is the simpler...