Back-to-back stemplot

A back-to-back stemplot runs one column of stems down the middle and hangs one group's leaves off each side. Both sides must use the same stem definition and the same place value, or the two halves are not on one scale. No values are discarded, so each group's median can still be counted straight off the display.

With 7 as the stem holding the tens digit, class A's row begins 2, 4, 5 counting outward from the spine, so those leaves are the values 72, 74 and 75, and on the page they print as 5, 4, 2 before you reach the stem. Class B's leaves of 1, 3 and 8 sit to the right and read in the ordinary direction as 71, 73 and 78. On both sides the smallest leaf is the one nearest the spine.

The error worth naming is a counting one. "Class A has 9 leaves on the stem of 7 and class B has only 7, so the 70s were more common in class A." A leaf count is a raw count, and raw counts only compare groups fairly when the groups are the same size. With 24 students in class A and 16 in class B, the shares are $9 / 24 = 0.375$ against $7 / 16 = 0.4375$, so the 70s are a larger part of class B despite its shorter row. Whenever the two sides have different totals, convert rows to proportions of their own group before comparing them.

The layout holds exactly two groups. A third needs a different display, and the plot stops being readable as $n$ grows, since a row of thirty leaves is a wall of digits rather than a shape. That is where a histogram or a side-by-side boxplot takes over.

The Fall 2026 course lists back-to-back stem-and-leaf plots in topic 1.9, among the displays used to compare the distributions of one quantitative variable across groups.