Bivariate Normal Datasets

A bivariate dataset consists of exactly two variables.
A a bivariate dataset is bivariate normal if it is univariate normal in any direction. In particular, both the x and y variables are univariate normal.
A bivariate dataset is also normally distributed in any thin rectangular strip in any direction.
The scatterplot of a bivariate dataset consists of an ellipse-shaped cloud of data points:
A parsimonious description of a bivariate normal dataset consists of five statistics: x, SD_x, y, SD_y, and r, where r is the correlation between x and y.
The point (x, y) is the center of gravity, also called the centroid, of the ellipse shaped cloud.
The dataset in the following scatterplot is not bivariate normal. In fact it is a collection of three separate bivariate normal groups.