Segmented Bar Chart vs Mosaic Plot

Each bar stands for one category of the first variable, and the pieces inside that bar show how that group divides across the second variable, which is its conditional distribution. When every bar is drawn to a common height of 100 percent, you compare segment sizes across bars to judge association. For example, if 30 of 50 freshmen play a sport but only 16 of 40 seniors do, the freshman bar is $30 / 50 = 0.60$ sport and the senior bar is $16 / 40 = 0.40$, so the two groups differ. If all the bars split in the same proportions, the two variables show no association in the sample.

A mosaic plot is a segmented bar chart with one extra piece of information: the width of each bar is proportional to how many observational units are in that group, so a tile's area is the share of the whole data set sitting in that cell. For example, with 150 freshmen and 50 seniors, the freshman bar takes $150 / 200 = 0.75$ of the width, and if 90 of those 150 freshmen play a sport that segment is $90 / 150 = 0.60$ of the bar's height. The tile area is then $0.75 \times 0.60 = 0.45$, matching the 90 of 200 students, or 45 percent, who are freshmen athletes. Heights let you compare groups, and areas tell you how much data stands behind each comparison.