Draw an ordered stem and leaf diagram with a key, then read off the median, mode and range from it. It is a Foundation topic, aimed at grade 2. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A stem-and-leaf diagram keeps the original data, just split: the stem is the leading digit(s), the leaf is the last digit. The key is not decoration — '4∣2 means 42' tells you that 5∣7 is 57, not 5.7. Leaves in each row must be in order, and a back-to-back diagram puts one data set on the left and one on the right of the same stems.
The range is still largest minus smallest, read from the diagram: if the values run from 13 to 29, the range is 16. The median is the middle leaf once you have counted how many values there are.
When you build one, write an unordered dump first if you need to, then rewrite with the leaves sorted. An unsorted row loses the 'ordered' mark.
Objectives
The stem is the rest of the number. The leaf is the last digit.
Leaves on a stem are written in order, smallest first.
A key such as 2 | 7 = 27 tells you the place value.
Key points
Split each value into a stem (usually the tens) and a leaf (the units).
Draw an ordered stem and leaf diagram with the leaves in size order and a key.
Read values back using the key.
Find the mode, median and range directly from the diagram.
Worked examples
Example 1
The marks of some pupils are shown in a stem-and-leaf diagram. The key is 1 | 2 means 12. The diagram is 1 | 2 5 8, then 2 | 1 4 4 9, then 3 | 0 3. What is the median mark?
2 marks
Rebuild the 9 marks using the key: 12, 15, 18, 21, 24, 24, 29, 30, 33.
The 5th value is the middle one = 24.
The median mark is 24.
Answer: 24
Common slips
Slip: Rebuild the 11 marks using the key: 12, 15, 18, 21, 24, 24, 29, 30, 33. That changes a number from the question, so it answers a different question.
Slip: The 8th value is the middle one = 24. That changes a number in the working, so the step no longer follows from the one before.
Slip: The median mark is 28. That does not match the working above it.
Example 2
The marks of some pupils are shown in a stem-and-leaf diagram. The key is 1 | 5 means 15. The diagram is 1 | 5 6 8, then 2 | 0 3 7 7, then 3 | 1. What is the range of the marks?
2 marks
The smallest mark is the first leaf: 15. The largest mark is the last leaf: 31.
Range = largest − smallest = 31 − 15 = 16.
The range is 16.
Answer: 16
Common slips
Slip: The smallest mark is the first leaf: 17. The largest mark is the last leaf: 31. That changes a number from the question, so it answers a different question.
Slip: Range = largest − smallest = 34 − 15 = 16. That changes a number in the working, so the step no longer follows from the one before.
Slip: The range is 20. That does not match the working above it.
Example 3
The marks of some pupils are shown in a stem-and-leaf diagram. The key is 2 | 1 means 21. The diagram is 2 | 1 7 9, then 3 | 0 2 5 5, then 4 | 4. What is the mode of the marks?
1 marks
Look for a leaf that repeats on the same stem. The repeated mark is 35.
35 appears 2 times and no other mark appears as often.
The mode is 35.
Answer: 35
Common slips
Slip: Look for a leaf that repeats on the same stem. The repeated mark is 37. That changes a number from the question, so it answers a different question.
Slip: 38 appears 2 times and no other mark appears as often. That changes a number in the working, so the step no longer follows from the one before.
Slip: The mode is 39. That does not match the working above it.
Questions and answers
GCSE Maths stem and leaf questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
In a stem-and-leaf diagram of masses in kg, the key is 1 | 3 means 1.3 kg. What mass does 2 | 2 show?
Show answer
Answer: 2.2 kg
The key puts the leaf after a decimal point: 1 | 3 is 1.3.
So stem 2 and leaf 2 is 2.2.
M1 — The key puts the leaf after a decimal point: 1 | 3 is 1.3.
A1 — Answer 2.2 kg
Question 2 Easy2 marks
The marks of some pupils are shown in a stem-and-leaf diagram. The key is 2 | 0 means 20. The diagram is 2 | 0 3 3 7, then 3 | 1 4 8, then 4 | 2 5. What is the median mark?
Show answer
Answer: 31
Rebuild the 9 marks using the key: 20, 23, 23, 27, 31, 34, 38, 42, 45.
The 5th value is the middle one = 31.
M1 — Rebuild the 9 marks using the key: 20, 23, 23, 27, 31, 34, 38, 42, 45.
A1 — Answer 31
Question 3 Medium2 marks
In a stem-and-leaf diagram of masses in kg, the key is 2 | 4 means 2.4 kg. What mass does 3 | 4 show?
Show answer
Answer: 3.4 kg
The key puts the leaf after a decimal point: 2 | 4 is 2.4.
So stem 3 and leaf 4 is 3.4.
M1 — The key puts the leaf after a decimal point: 2 | 4 is 2.4.
A1 — Answer 3.4 kg
Question 4 Medium2 marks
The marks of some pupils are shown in a stem-and-leaf diagram. The key is 1 | 4 means 14. The diagram is 1 | 4 6 9, then 2 | 2 2 5 8, then 3 | 1 6. What is the median mark?
Show answer
Answer: 22
Rebuild the 9 marks using the key: 14, 16, 19, 22, 22, 25, 28, 31, 36.
The 5th value is the middle one = 22.
M1 — Rebuild the 9 marks using the key: 14, 16, 19, 22, 22, 25, 28, 31, 36.
A1 — Answer 22
Question 5 Hard2 marks
In a stem-and-leaf diagram of masses in kg, the key is 3 | 5 means 3.5 kg. What mass does 4 | 6 show?
Show answer
Answer: 4.6 kg
The key puts the leaf after a decimal point: 3 | 5 is 3.5.
So stem 4 and leaf 6 is 4.6.
M1 — The key puts the leaf after a decimal point: 3 | 5 is 3.5.
A1 — Answer 4.6 kg
Question 6 Hard2 marks
The marks of some pupils are shown in a stem-and-leaf diagram. The key is 3 | 5 means 35. The diagram is 3 | 5 8, then 4 | 0 1 4 4 9, then 5 | 3 6. What is the median mark?
Show answer
Answer: 44
Rebuild the 9 marks using the key: 35, 38, 40, 41, 44, 44, 49, 53, 56.
The 5th value is the middle one = 44.
M1 — Rebuild the 9 marks using the key: 35, 38, 40, 41, 44, 44, 49, 53, 56.
A1 — Answer 44
Question 7 Exam-style2 marks
The marks of some pupils are shown in a stem-and-leaf diagram. The key is 1 | 0 means 10. The diagram is 1 | 0 3 7, then 2 | 3 6 6 8, then 3 | 2 9. What is the median mark?
Show answer
Answer: 26
Rebuild the 9 marks using the key: 10, 13, 17, 23, 26, 26, 28, 32, 39.
The 5th value is the middle one = 26.
The median mark is 26.
M1 — Rebuild the 9 marks using the key: 10, 13, 17, 23, 26, 26, 28, 32, 39.
A1 — Answer 26
Common mistakes
Most lost marks on this topic are one slip.
Reading the stem as the whole number.
Put the leaf back on, using the key.
Finding the median before the leaves are in order.
Order each stem first.
Ignoring the key and treating 2 | 7 as 2.7 when the key says 27.
The key decides the place value.
Spot the slip
In a stem-and-leaf diagram the leaf of 27 is
7
2
27
Show the slip
7 The leaf is the units digit.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Cross off each data value as you place it; then count leaves against the number of values before you finish.
Draw the unordered diagram in rough and the ordered one neatly — the question usually asks for ordered.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.