1. Stem & Leaf Diagrams
What is it, and why bother?
Imagine you have a messy list of ages: 11, 18, 20, 21, 25, 28, 29, 35, 36, 40. A stem-and-leaf diagram
is a clever way to organise this list without losing any of the actual data — unlike
a bar chart, which only shows you frequencies and throws away the individual values.
Every two-digit number gets split into two parts:
- The stem = the tens digit (written once, vertically, on the left)
- The leaf = the units digit (written horizontally, in increasing order, next to its stem)
So 25 becomes 2 | 5. Here's the full diagram for the ages above:
Age
1 | 1 8
2 | 0 1 5 8 9
3 | 5 6
4 | 0
Key: 1|8 means 18 years old
Why this matters
Notice the leaves are in order (1, 8 not 8, 1) — this ordering is what makes it so easy to find
the median later. A stem-and-leaf diagram is basically "sorted data in disguise."
The Key
The key is not optional decoration — without it, nobody (including you, a week later) knows what
the digits mean. It tells you exactly how to rebuild a value from its stem and leaf, and it must
include units.
The key can represent very different things depending on context:
- 2 | 5 could mean 25 years old
- 2 | 5 could mean 2.5 degrees
- 2 | 5 could mean 2500 people (if the stem represents thousands)
Always read the key before you read the diagram — it changes everything.
Finding the Median from a Stem & Leaf Diagram
Because the data is already sorted in order, finding the median is just a matter of locating the middle value.
Method: Cross out one value from each end (first and last) simultaneously, working inward, until you
land on the middle number (or the middle two numbers).
If two numbers remain in the middle, the median is the midpoint (average) of the two.
Classic mistake
Students often write down only the leaf as the answer (e.g. "median = 6") instead of
rebuilding the full number using its stem too (median = 26). The stem is part of the value — don't drop it!
Worked Example
A hospital records blood pressure reduction (mmHg) for 11 patients:
12, 31, 24, 18, 21, 34, 40, 19, 23, 17, 16
Step 1 — Split each value into stem (tens) and leaf (units), unsorted first:
| Stem | Leaf (unsorted) |
|---|
| 1 | 2 8 9 7 6 |
| 2 | 4 1 3 |
| 3 | 1 4 |
| 4 | 0 |
Step 2 — Reorder each row so leaves increase left to right:
| Stem | Leaf (ordered) |
|---|
| 1 | 2 6 7 8 9 |
| 2 | 1 3 4 |
| 3 | 1 4 |
| 4 | 0 |
Key: 1|2 means a blood pressure reduction of 12 mmHg.
Step 3 — Find the median. There are 11 values, so the median is the 6th value.
Counting along: 12, 16, 17, 18, 19, 21... the 6th value is 21 (stem 2, leaf 1).
Median = 21 mmHg
Practice Question 1
The shoe sizes (as whole numbers) of 9 students are: 7, 6, 8, 6, 9, 5, 8, 7, 6.
Draw an ordered stem-and-leaf diagram (using stem = whole number, leaf = 0 for these single-digit
numbers won't quite work — instead treat this as: sort the data and find the median directly).
What is the median shoe size?
Practice Question 2
A stem-and-leaf diagram has stem 3 with leaves 2, 5, 5, 8 and stem 4 with leaves 0, 1, 3.
Key: 3|2 means 32. Find the median of all 7 values.