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Stem-and-Leaf Diagrams

FoundationHigherAQAEdexcelOCR

Practise stem-and-leaf diagrams with this free Foundation and Higher GCSE Maths worksheet from Virtus Academy. You'll work through reading stem-and-leaf diagrams, building confidence for your exam, and every question comes with worked solutions in the mark scheme. Suitable for AQA, Edexcel and OCR. Always include a key so the values can be read correctly.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A stem-and-leaf diagram displays data while keeping every original value visible, unlike a grouped frequency table.

The stem holds the leading digits and the leaf holds the final digit. So a stem of \(3\) with leaves \(2\), \(5\) and \(7\) represents the values \(32\), \(35\) and \(37\).

A key is essential and carries a mark on its own. Without it, a stem of \(3\) and a leaf of \(2\) could mean \(32\), \(3.2\) or \(320\). The leaves must also be written in order, which makes the median easy to find.

Revision notes

Structure and key

The stem shows the leading digits and the leaf the final digit, with a key such as \(3 \mid 2\) means \(32\).

The key must always be given, and it is worth a mark in itself.

Ordering the leaves

Write the leaves in ascending order within each row.

This makes the diagram an ordered list of the data, so the median and quartiles can be counted off directly.

Finding averages

Count through the leaves to find the median, exactly as with any ordered list.

The mode is the most frequently repeated leaf within a stem, and the range is the largest value minus the smallest.

Key points

  • The stem holds the leading digits.
  • The leaf holds the final digit.
  • A key is essential and carries a mark.
  • Leaves are written in ascending order.
  • Every original value is preserved.
  • The median can be counted off directly.

Worked examples

Example 1

A stem of \(4\) has leaves \(1, 3, 8\). Write the values.

Working

\[\text{Stem gives the tens, leaf the units}\]apply the structure
\[41, 43, 48\]state the values

Example 2

Why must a stem-and-leaf diagram have a key?

Working

\[3 \mid 2 \text{ could mean } 32, 3.2 \text{ or } 320\]the value is ambiguous
\[\text{The key removes the ambiguity}\]state the reason

Example 3

A diagram has \(15\) values. Find the position of the median.

Working

\[\frac{15+1}{2}\]use the position formula
\[= 8\text{th value}\]count through the ordered leaves

Common mistakes

  • Omitting the key.

    It carries a mark and without it the values are ambiguous.

  • Writing the leaves out of order.

    They must be ascending within each stem so the diagram is an ordered list.

  • Writing more than one digit as a leaf.

    The leaf is a single digit; extra digits belong in the stem.

  • Forgetting a repeated value.

    Every occurrence needs its own leaf, even if the digit repeats.

Exam tips

  • Always include a key, written as stem bar leaf means the value.
  • Order the leaves within each row.
  • Count through the leaves to find the median.
  • Use one digit per leaf.

Key terms

Stem
The leading digits of a value.
Leaf
The final digit of a value.
Key
A statement showing how to read the diagram.
Ordered
Arranged from smallest to largest.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.