Stem-and-Leaf Diagrams
Master Stem-and-Leaf Diagrams for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Stem-and-leaf diagrams display ordered data while keeping the original values, so the median and shape are easy to read.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
Topic overview
A stem-and-leaf diagram displays data in order while keeping every individual value visible, which is its main advantage over a grouped frequency table.
The stem is the leading digit or digits and the leaf is the final digit. A value of 47 has stem 4 and leaf 7. Leaves are written in order across each row, and a key must always be included to show how to read the values.
Because the data is ordered and all values are retained, the median, mode and range can all be found exactly. A back-to-back stem-and-leaf diagram compares two data sets using one stem, with leaves extending in opposite directions and read outwards from the stem in each case.
Revision notes
Structure and key
The stem holds the leading digits and the leaf the final digit.
Leaves are written in ascending order across each row. A key is essential — for example, 4 | 7 means 47. Without a key the diagram cannot be interpreted.
Finding statistics
Because every value is retained and already in order, the median, mode and range can all be found exactly.
Count to the middle position for the median. The mode is the most repeated leaf within a stem. The range is the largest value minus the smallest.
Back-to-back diagrams
Two data sets share a single central stem, with leaves extending left and right.
The left-hand leaves are read outwards from the stem, so they run right to left and increase away from the centre. This is the detail most often misread.
Key points
- The stem holds the leading digits.
- The leaf holds the final digit.
- Leaves are written in ascending order.
- A key is always required.
- All individual values are retained.
- Back-to-back diagrams compare two sets.
Worked examples
Example 1
A stem-and-leaf diagram has the row 3 | 2 5 7 9. The key is 3 | 2 means 32. Work out the range of this row. [2 marks]
Working
Example 2
Explain one advantage of a stem-and-leaf diagram over a grouped frequency table. [2 marks]
Working
Example 3
Explain why a key is essential on a stem-and-leaf diagram. [2 marks]
Working
Common mistakes
Forgetting the key.
Without it the values are ambiguous and marks are lost.
Writing leaves out of order.
They must be in ascending order across each row.
Reading back-to-back leaves in the wrong direction.
Left-hand leaves increase outwards from the central stem.
Writing more than one digit as a leaf.
The leaf is a single digit; extra digits belong in the stem.
Exam tips
- Always include and use the key.
- Write leaves in ascending order.
- Read left-hand leaves outwards from the stem.
- Use the retained values to find exact statistics.
Key terms
- Stem
- The leading digits of a value.
- Leaf
- The final digit of a value.
- Key
- A guide showing how to read stem and leaf together.
- Back-to-back
- Two data sets sharing one central stem.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.