Stem and leaf diagrams Revision Notes for Edexcel GCSE Statistics

Stem and leaf diagrams

What are stem and leaf diagrams?

A stem and leaf diagram is a method of displaying data that shows you the distribution of individual values whilst keeping the original data visible. Think of it as an organised way to arrange numbers so you can easily spot patterns, find the most common values, and see how spread out your data is.

The diagram works by splitting each number into two parts:

The stem contains the tens (or higher place values)
The leaves contain the units (ones) and must always be single digits

For example, if you have the number 35, the stem would be 3 and the leaf would be 5.

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Stem and leaf diagrams are particularly useful because they preserve all the original data values while still showing you the shape and pattern of your data distribution - something that other types of charts like histograms cannot do.

Understanding the key

Every stem and leaf diagram needs a key to help you interpret what the numbers mean. The key shows you:

What each stem and leaf combination represents
The units being measured

For instance, if your key says "3|5 represents 35 emails", this tells you that a stem of 3 with a leaf of 5 means 35 emails.

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The key is not optional - without it, your diagram becomes meaningless! Always include a clear key that shows both the numerical interpretation and the units of measurement.

How to read a stem and leaf diagram

Understanding how to interpret a stem and leaf diagram is essential for extracting meaningful information from your data.

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Reading Example: Email Data

Let's look at an example showing the number of emails 15 people received in one day:

    0 | 6   8
    1 | 2   2   4   6
    2 | 0   2   3   4   7   7
    3 | 1   3   5

Key: 3|5 represents 35 emails

From this diagram, you can see:

One person received 6 emails, another received 8
Four people received between 12-16 emails
Six people received between 20-27 emails
Three people received between 31-35 emails

The leaves are arranged in order from smallest to largest, making it easy to spot patterns and find measures like the median.

Back-to-back stem and leaf diagrams

When you need to compare two sets of data, you can create a back-to-back stem and leaf diagram. This places both sets of data on either side of the same stem, allowing for easy comparison.

In a back-to-back diagram:

The stem goes in the middle column
One set of data has leaves on the left
The other set has leaves on the right
The smallest values in each row are placed closest to the stem

Here's an example comparing test scores:

Test 1          |    | Test 2
    6  4  3  1  | 6  | 3  5  7  9  9
       8  3  2  | 7  | 5  5
       6  3  0  | 8  | 7  7  9

Key: 6|5 = 56    5|7 = 57

This shows that Test 2 generally had higher scores than Test 1.

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Back-to-back diagrams make it immediately obvious which data set has higher or lower values, and you can easily compare the spread and distribution of both sets at a glance.

How to draw a stem and leaf diagram: step-by-step method

Creating an accurate stem and leaf diagram requires a systematic approach to avoid errors and ensure all data is properly represented.

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Worked Example: Goals Scored

Let's work through creating a stem and leaf diagram using this data set - goals scored by a player in 20 games: 23, 9, 20, 14, 23, 6, 17, 24, 24, 18, 16, 10, 22, 21, 11, 8, 21, 15, 8, 22

Step 1: Identify your stems Look at your data and decide what stems you need. For this data (ranging from 6 to 24), you'll need stems: 0, 1, 2

Step 2: Create an unordered diagram first Go through your data in the original order and place each number:

Use 0, 1, and 2 for the stems
Cross off each number in your original list as you copy it to avoid missing any

0 | 9  6  8  8
1 | 4  7  8  0  1  5
2 | 3  0  3  4  4  2  1  1  2

Step 3: Reorder the leaves Now rewrite the diagram with leaves in increasing order for each row:

0 | 6  8  8  9
1 | 0  1  4  5  6  7  8
2 | 0  1  1  2  2  3  3  4  4

Key: 2|0 represents 20 goals

Step 4: Include the key Always remember to include a key that clearly shows what the stem and leaf combination represents, including the units.

Common exam tips and traps

Understanding common pitfalls will help you create accurate diagrams and avoid losing marks in examinations.

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Always remember:

Leaves must be single digits only - if you have a number like 127, the stem is 12 and the leaf is 7
Include a clear key with units
Order the leaves from smallest to largest in the final diagram
Cross off numbers as you copy them to avoid mistakes
In back-to-back diagrams, put the smallest values closest to the stem

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Common mistakes to avoid:

Forgetting to include a key
Not ordering the leaves properly
Using multiple digits as leaves
Missing numbers when copying from the original data

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Key Points to Remember:

Stem and leaf diagrams display individual data values whilst showing the overall distribution pattern
Leaves must always be single digits - this is a fundamental rule you cannot break
Always include a key that shows what stem|leaf represents, including the correct units
Start with an unordered diagram and cross off numbers as you go, then reorder the leaves from smallest to largest
Back-to-back diagrams are perfect for comparing two data sets using the same stems, with smallest values placed nearest to the central stem

Stem and leaf diagrams (Edexcel GCSE Statistics): Revision Notes