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GCSE Maths · Statistics
Stem-and-leaf diagrams GCSE Questions and Worked Answers
A stem-and-leaf diagram splits each recorded value into a shared leading part and a final digit. It organises the data while retaining every individual value; the key explains how to rejoin the parts.
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Start with the meaning
What you need to know about stem-and-leaf diagrams
Suppose six journey times are 12, 15, 15, 21, 24 and 30 minutes. Instead of writing the tens digit repeatedly, group together times that start with the same tens digit. Write that digit on the left: it is the stem. Write each remaining ones digit on the right: it is a leaf. The two 15-minute journeys still need two leaves, because two separate observations were recorded.
See the idea first
Keep each value, including repeats
The row 1 | 2 5 5 represents 12, 15 and 15, not the number 1255. Leaves are ordered from smallest to largest within each row. The key 2 | 4 = 24 minutes defines both place value and units; a different key could instead make that entry mean 2.4.
| Stem (tens) | Leaves (ones), in order |
|---|---|
| 1 | 2 5 5 |
| 2 | 1 4 |
| 3 | 0 |
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Construct a diagram
What the problem asks: Organise 23, 17, 21, 17 and 30.
How to solve it: Sort to 17, 17, 21, 23, 30. Rows are 1 | 7 7; 2 | 1 3; 3 | 0. Add a key such as 2 | 3 = 23.
Find the median
What the problem asks: Find the median of the six journey times in the diagram.
How to solve it: The third and fourth values are 15 and 21, so median = (15 + 21)/2 = 18 minutes. Count leaves, not stems.
Compare two groups
What the problem asks: One group has median 18 and range 8; another has median 22 and range 5 minutes. Compare their times.
How to solve it: The first group is typically quicker but less consistent. Use both a measure of centre and a measure of spread, in context.
A reliable routine
Build an ordered stem-and-leaf display
Use this method for a manageable list of numerical observations. Each leaf stores one final digit, preserving individual values for later calculations.
- Choose the place-value split and write a key with units.
- List stems in order, including empty intermediate stems if needed.
- Write one leaf per observation and sort leaves within each row.
- Count leaves to check none was lost; reconstruct whole values before calculating statistics.
Check: Edexcel's S2 guidance explicitly includes these diagrams. OCR states that prior knowledge of stem-and-leaf diagrams is not required. Back-to-back diagrams share stems; on the left, leaves increase as you move away from the stem, so their printed order is reversed.
Fully worked
Stem-and-leaf diagrams GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Decode a row
Question
Using key 2 | 4 = 24 minutes, decode 3 | 1 1 8.
The stem gives thirty and the leaves give ones. Values: 31, 31, 38 minutes. Preserve the repeated 31.
Example 2
Construct
Question
Draw a stem-and-leaf diagram for 12, 15, 15, 21, 24, 30 minutes.
Use stems 1, 2 and 3; leaves 2 5 5, then 1 4, then 0. Include key 2 | 4 = 24 minutes.
| Stem (tens) | Leaves (ones), in order |
|---|---|
| 1 | 2 5 5 |
| 2 | 1 4 |
| 3 | 0 |
Example 3
Median from leaves
Question
Find the median of the displayed journey times.
| Stem (tens) | Leaves (ones), in order |
|---|---|
| 1 | 2 5 5 |
| 2 | 1 4 |
| 3 | 0 |
Six leaves mean six values. The middle positions are 3 and 4, holding 15 and 21.
Example 4
Mode and range
Question
Find the mode and range of the displayed times.
| Stem (tens) | Leaves (ones), in order |
|---|---|
| 1 | 2 5 5 |
| 2 | 1 4 |
| 3 | 0 |
15 appears twice; every other value appears once. Mode: 15 minutes.
Example 5
Decimal key
Question
A diagram has key 4 | 2 = 4.2 kg. Decode 5 | 0 3 8.
The stem gives whole kilograms; each leaf gives tenths. Values: 5.0, 5.3, 5.8 kg.
Example 6
Back-to-back order
Question
Values in group A are 21, 24, 28; in group B they are 22, 25. Show the shared stem row using A on the left.
Read outwards from the stem on each side. A leaves: 8 4 1 | stem 2 | B leaves: 2 5. Key: left 1 | 2 means 21; right 2 | 2 means 22. Leftmost 8 still represents 28, not 82.
10 original questions · total 20 marks
Stem-and-leaf diagrams GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 25 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
Key
With 3 | 6 = 36 cm, decode 4 | 2.
Show worked answer
42 cm: four tens and two ones.
List values
With 1 | 2 = 12, decode 2 | 0 4 4 9.
Show worked answer
20, 24, 24, 29. Each leaf is a separate value.
Sort leaves
Stem 3 has leaves 7, 1, 5, 1. Write the ordered row.
Show worked answer
3 | 1 1 5 7. Keep both 1s.
Count observations
Stems 1, 2 and 3 have 3, 5 and 2 leaves. How many observations?
Show worked answer
Odd median
A diagram represents 11, 13, 18, 22, 29. Find median.
Show worked answer
Five values give middle position 3. Median: 18.
Even median
A diagram represents 8, 12, 15, 19, 21, 25. Find median.
Show worked answer
Average positions 3 and 4.
Range
Using key 1 | 2 = 12, the smallest entry is 1 | 4 and largest 4 | 1. Find range.
Show worked answer
Reconstruct 14 and 41 first.
Repeated values
A dataset contains three observations equal to 26. How many leaves 6 belong on stem 2?
Show worked answer
Three leaves. Removing repeated values would change the dataset.
Empty stem
Represent 12, 18, 31 using tens as stems.
Show worked answer
Rows: 1 | 2 8; 2 | (empty); 3 | 1. Add key 1 | 2 = 12. The empty row shows no twenties.
Compare samples
Group A has median 14 and range 10 minutes; B has median 17 and range 6. Compare typical time and consistency.
Show worked answer
A has a lower median, so is typically 3 minutes quicker. B has a smaller range, suggesting more consistent times. These summaries do not mean every A time is below every B time.
Examiner-style feedback
Common stem-and-leaf diagrams mistakes
Each measurement gets its own leaf.
Readers cannot infer units or decimal placement reliably.
Reconstruct complete values before finding a median or range.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
- Define the key.
- Order stems and leaves.
- Keep every observation.
- Count positions carefully.
Quick answers
Stem-and-leaf diagrams FAQ
Are these diagrams needed for every exam board?
No. Edexcel explicitly includes them; OCR does not require prior knowledge. Check your own specification.
Can leaves have two digits?
Each leaf is one digit in the usual convention; choose the stem and key accordingly.
Content standards
Curriculum and rights review
S2 representation and S4 summaries; explicitly included by Pearson Edexcel guidance, not required prior knowledge for OCR. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
Official specification references