Histograms and probability density functions

The situation is a little more complicated for continuous numerical populations and samples. A standard histogram could be used to describe the population in the same way that it might be used for a sample:

However with an infinite population, we can narrow the histogram classes beyond what would be reasonable for a finite sample. Indeed, class widths can be reduced indefinitely, resulting in a smooth histogram called a probability density function. This is often abbreviated to a pdf.

Probability density functions are still essentially histograms and share all properties of histograms.