A stem and leaf diagram organises numerical data by place value while keeping every original value visible. The stem is the leading digit(s); the leaf is always a single final digit. For $52$: stem $5$, leaf $2$. For a three-digit number like $369$: stem $36$, leaf $9$. For a decimal like $2.7$: stem $2$, leaf $7$ — the key (e.g. $2|7 = 2.7$) is what tells you where the decimal point actually goes, so without it the diagram is meaningless.

1. Sort the raw data into ascending order first — this isn't optional, since everything afterwards depends on it.
2. List every stem the data spans, in order, including any stem with no leaves (omitting one creates a false impression that the data has no gap there).
3. Write each leaf next to its stem, in ascending order, with no punctuation between digits.
4. Add the key underneath, with units if relevant.

Example: ordering $18, 25, 28, 29, 29, 33, 35, 36, 40, 45$ gives:

Key: $2|5$ represents $25$.

Because the diagram is already ordered, these fall out directly: the mode is the most-repeated leaf on one stem; the median sits at position $\tfrac{n+1}{2}$ (counting leaves from the top), averaging the two middle values if $n$ is even; the range is (highest value) $-$ (lowest value), read straight from the first and last leaves.

A back-to-back plot shares one central stem column, with one dataset's leaves to the left (written in ascending order moving outward, right to left) and the other's to the right (ordinary left-to-right order). Both datasets must be sorted before plotting, and the key must explain both sides. This layout lets you compare medians, ranges and overall shape (e.g. "Team A has a higher median and a smaller range, suggesting more consistent higher scores") directly from the same diagram.

12 students' test scores are: $34, 41, 28, 35, 47, 33, 29, 41, 38, 35, 44, 29$. Construct an ordered stem and leaf diagram and find the median and range.

Ordered: $28,29,29,33,34,35,35,38,41,41,44,47$.

Key: $3|4 = 34$. With $n=12$, median position $=6.5$, averaging the 6th ($35$) and 7th ($35$) values: median $=35$. Range $=47-28=\mathbf{19}$.