Section B clusters in the 70s and 80s , Section A spreads wider with more extreme values on both ends Figure 68.1 , Section B clusters in the 70s and 80s

A Stem and Leaf Plot organises a dataset by its place values. Each value is split into a stem (the leading digit or digits, typically representing the tens place) and a leaf (the trailing digit, representing the ones place). Stems are arranged in ascending order in a central column; leaves extend horizontally from their corresponding stem. The defining property is losslessness : every original data value is preserved in full and can be reconstructed exactly by combining its stem and leaf.

When two datasets share the same stem values, they can be displayed back-to-back: one dataset's leaves extend to the left, the other's to the right. The stems occupy the shared central column. This allows direct visual comparison of two distributions at every stem level simultaneously , the viewer reads one dataset's shape from right to left and the other from left to right, and the asymmetry between them is immediately visible. The back-to-back stemplot is the simplest multi-dataset comparison tool that preserves every data value.

The message compares two class sections' exam score distributions. The dataset is small enough (25, 30 values per section) that every data point can be displayed without overcluttering , this is the stemplot's optimal range. Binning the data into a histogram would lose the exact scores; a box plot would reduce each section to five numbers and hide the clustering pattern in the 70s and 80s.

The stemplot has hard practical limits in both directions. With fewer than 10, 15 values, most stem rows contain 0, 1 leaves; the "distribution" is too sparse to have a shape, and a simple sorted list is more useful. With more than 50, 80 values per dataset, stem rows become crowded with 10+ leaves, the display wraps, and the visual distribution signal is lost in a wall of digits.

Paste this into Claude Code to generate a working version of this chart, plus its data file. The result will not be a perfect replica , the goal is that the reader can run the prompt, get a chart of this type, and read its source. Generate a complete, self-contained stem leaf in D3 v7. Two files:

The ideas in this chapter didn't appear from nowhere. Arthur Lyon Bowley was a British statistician who in 1901 produced Elements of Statistics , the first English-language statistics textbook to systematically use simple visual displays (including a precursor to stem-and-leaf and dot displays) to teach inferential reasoning. Arthur Lyon Bowley, circa 1920. AI-generated portrait based on a public domain photograph (Wikimedia Commons).

The ideas in this chapter didn't appear from nowhere. Arthur Lyon Bowley was a British statistician who in 1901 produced Elements of Statistics , the first English-language statistics textbook to systematically use simple visual displays (including a precursor to stem-and-leaf and dot displays) to teach inferential reasoning. Arthur Lyon Bowley, circa 1920. AI-generated portrait based on a public domain photograph (Wikimedia Commons).