Using histograms to examine the distribution of continuous variables

The go-to visualization tool for statisticians trying to understand how single variables are distributed is the histogram. Histograms plot a continuous variable on the x axis, in bins determined by the researcher, and the frequency of occurrence on the y axis.

Histograms provide a clear and meaningful illustration of the shape of a distribution, including central tendency, skewness (symmetry), excess kurtosis (relatively fat tails), and spread. This matters for statistical testing, as many tests make assumptions about a variable's distribution. Moreover, our expectation of what data values to expect should be guided by our understanding of the distribution's shape. For example, a value at the 90th percentile has very different implications when it comes from a normal distribution rather than from a uniform distribution.

One of the first tasks I ask introductory statistics students to do is construct...