Stem & Leaf Diagrams (Cambridge (CIE) IGCSE Maths: Extended): Revision Note
Exam code: 0580 & 0980
Stem & leaf diagrams
What is a stem-and-leaf diagram?
A stem-and-leaf diagram is a simple way to display an ordered list of data using digits
Two-digit numbers are split into a tens digit (the stem) and a units digit (the leaf)
25 becomes 2 | 5
The stem is written vertically and the leaves are written horizontally (in order)
The following diagram shows the ages below
11, 18, 20, 21, 25, 28, 29, 35, 36, 40
| Age |
1 | 1 8 |
2 | 0 1 5 8 9 |
3 | 5 6 |
4 | 0 |
Key: 1|8 means 18 years old
What is the key on a stem-and-leaf diagram?
The key shows how values are formed from digits
It should include units
Other keys are possible
2 | 5 represents 2.5 degrees
2 | 5 represents 2500 people
How do I find the median from a stem-and-leaf diagram?
The median is the middle number
Data values are already in order
You can cross out numbers from the beginning and end until they meet in the middle
Remember that the highest number will be at the end of the last stem
If two numbers remain in the middle, find the midpoint between them
Examiner Tips and Tricks
A common mistake when finding the median is to write down the leaf only (median = 6) rather than the stem and leaf (median = 26).
Worked Example
A hospital is investigating a new drug that claims to reduce blood pressure.
The reductions in blood pressure, measured in mmHg (millimetres of mercury), for 11 patients are shown below.
12 31 24 18 21 34 40 19 23 17 16
(a) Draw a stem and leaf diagram to show these results.
Answer:
Split each value into its tens digit (stem) and units digit (leaf)
The values are not yet in order
| Blood pressure reduction |
1 | 2 8 9 7 6 |
2 | 4 1 3 |
3 | 1 4 |
4 | 0 |
Put the values in order
Write down the key
| Blood pressure reduction |
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
(b) Use your stem and leaf diagram to find the median blood pressure reduction.
Answer:
Find the middle value
This is the 6th patient
| Blood pressure reduction |
1 | 2 6 7 8 9 |
2 | 3 4 |
3 | 1 4 |
4 | 0 |
The median has a leaf of 1 and a stem of 2
The median is 21 mmHg
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Questions students ask about Stem & Leaf Diagrams
Real questions from students revising this topic on Save My Exams
How do you find the median from a stem-and-leaf diagram?
The data in a stem-and-leaf diagram is already in order, so cross off values from each end until you reach the middle — then write it using both the stem and the leaf.
- Count the leaves to see how many values there are.
- Cross off the first leaf on the top stem and the last leaf on the bottom stem, and keep going in pairs.
- If one leaf is left, that's the median. If two are left, find the midpoint (add them and divide by 2).
- Use the key to write the full value.
Worked example (from this page): blood pressure reductions for 11 patients
1 | 2 6 7 8 9 2 | 1 3 4 3 | 1 4 4 | 0 Key: 1|2 means 12 mmHg
- 11 leaves, so cross off 5 from each end and the middle is the 6th value.
- Counting along: 12, 16, 17, 18, 19, then 21.
- Stem 2, leaf 1, so the median is 21 mmHg.
Common mistake: writing just the leaf (1) instead of the full value (21). Shortcut: for n values the median is the (n + 1)/2 th.
How do you draw a stem-and-leaf diagram?
Split each number into a stem (the tens digit) and a leaf (the units digit), write the stems down the side and the leaves in order along each row, then add a key with units.
- Choose the stems. Look at the smallest and largest values and write every tens digit between them down a vertical line.
- Add the leaves. Work through the data, writing each units digit next to its stem — 25 becomes 2 | 5.
- Order the leaves. Redraw each row with its leaves smallest to largest.
- Write a key, including units.
Worked example (from this page): 12, 31, 24, 18, 21, 34, 40, 19, 23, 17, 16
Unordered: 1 | 2 8 9 7 6 2 | 4 1 3 3 | 1 4 4 | 0
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
Tip: count your leaves at the end — there should be one per data value (11 here).
How do you find the interquartile range from a stem-and-leaf diagram?
Read the lower and upper quartiles off the ordered diagram in the same way as the median, then subtract: IQR = upper quartile − lower quartile.
- Find the median (the middle value).
- Lower quartile (LQ): the middle of the values below the median.
- Upper quartile (UQ): the middle of the values above the median.
- IQR = UQ − LQ
Worked example (using this page's diagram):
1 | 2 6 7 8 9 2 | 1 3 4 3 | 1 4 4 | 0 Key: 1|2 means 12 mmHg
- In order: 12, 16, 17, 18, 19, 21, 23, 24, 31, 34, 40
- Median = 21 (the 6th value)
- Lower half 12, 16, 17, 18, 19 → LQ = 17
- Upper half 23, 24, 31, 34, 40 → UQ = 31
- IQR = 31 − 17 = 14 mmHg
Tips: with 11 values the quartiles are the 3rd and 9th, so you can count leaves straight to them. Always write the full value, and keep the units.
