Data Science Live Book

Dashed-line represents variable mean.

Density histograms are nice to visualize the general shape of a numeric distribution.

This general shape is calculated based on a technique called Kernel Smoother, its general idea is to reduce high/low peaks (noise) present in near points/bars by estimating the function that describes the points. Here some pictures to illustrate the concept:

A kernel smoother is a statistical technique for estimating a real valued function {\displaystyle f(X)\,\,\left(X\in \mathbb {R} ^{p}\right)} by using its noisy observations, when no parametric model for this function is known. The estimated function is smooth, and the level of smoothness is set by a single parameter.

Something similar is what an statistical test sees: they measured how different the curves are reflecting it in some statistics (like the p-value), in order to give to the analyst, a reliable information to determine if the curves have -for example- the same mean.