The ellipse plot is a family of box and whisker plot, and resembles to the double box plot. An ellipse plot of five number summary is given with following steps.
Centers of ellipses are bounded to the median. To do that, an ellipse here strictly is not a single ellipse.
An ellipse here is synthesized from four quarter ellipses. As shown in Figure 3, a box is divided into four rectangles by lines through the median. A quarter ellipse is drawn for each rectangle. The bluish rectangle is indicating one of these quarters.
Ellipses are drawn from the center (median) to outward of quantiles.
For quartiles (five number summary), following two ellipses are drawn.
For octiles (nine number summary), following four ellipses are drawn.
Benefits of using the ellipse plot come from benefits of quantile summary. Figure 4 shows a comparison between ellipse plots and scatter plots.
A distribution shape is clearer at the ellipse plot, because the information is organized. A raw scatter plot is too sparse when the sample number is small, and is too overstuffed when the sample number is large (Figure 4).
Comparing with a double box plot, an ellipse plot is useful when comparing distributions because its shape is simple. Though a double plot is tightly binded with five number summary, an ellipse plot can use other quantiles, nine number summary and more (Figure 5).
An ellipse plot looks like something like a integrated histogram of x and y axes (Figure 6).
But it is not.
Figure 7 shows an ellipse plot of a normal distributed data set (x) and a uniform distributed (white noise) data set (y). Though the histogram of y axis is flat, the ellipse plot shows a triangular peak along y axis.
So, an ellipse plot shows a steeper slope toward the center. This indicates an integrate from the center to outside, that is the cumulative distribution.