In many places during this course we will assume that a sample comes from a population having the normal (bell-shaped) distribution. A plot based on percentiles that seeks to verify this assumption is called the normal quantile plot. This is a scatterplot of the percentiles of the data versus the percentiles of a population in fact having the normal distribution. If the data do come from a normal population, the resulting points should fall closely along a straight line.
To illustrate this, the figure below shows the normal quantile plot of a random sample of 50 IQ's (we said earlier that IQ's do in fact follow a normal distribution). Notice how the points closely follow the line.
To better understand the information that the normal quantile plots provide us and the relationship among distributions , histograms, box plots and normal quantile plots, we can look at the figure at the previous page. The 4 plots on the first row indicate the distributions where the data are sampled from. The second, the third and the fourth rows are, respectively, the corresponding histograms, boxplots and normal quantile plots. The four distributions are normal, long tailed, short tailed and skewed, respectively.