What does the key mean in a stem and leaf diagram?

The key explains how the stem and leaf combine to form a complete value. For example, $3\mid7=37$ means stem $3$ and leaf $7$ represent $37$. If the data contain decimals, a key such as $3\mid7=3.7$ shows that the leaf represents tenths.

Do the leaves have to be in order?

In an **ordered stem and leaf diagram**, the leaves must be arranged from smallest to largest within each row. This makes the median, minimum and maximum easier to identify. GCSE questions commonly ask specifically for an ordered diagram.

How do you find the median from a stem and leaf diagram?

Count all the leaves to find the number of observations, then locate the middle value in the ordered diagram. If there is an even number of observations, calculate the mean of the two middle values.

How do you find the frequency from a stem and leaf diagram?

Count the leaves. Each leaf represents one observation, including repeated leaves. To find the frequency of a particular group, count only the leaves in the relevant row.

Can a stem and leaf diagram contain decimals?

Yes. The key defines the place value. For example, $2\mid6=2.6$ means the stem represents units and the leaf represents tenths. Never assume that $2\mid6$ means $26$ without checking the key.

Should an empty stem be included?

Usually, yes. If the stems run from $1$ to $3$ but there are no values with stem $2$, include the stem $2$ with an empty leaf row. This preserves the continuous numerical scale and shows the gap clearly.

Stem and Leaf Diagrams GCSE Maths Revision Guide

Stem and leaf diagrams GCSE Maths questions test whether you can organise numerical data while keeping every original value visible. At Foundation tier, you may need to complete or draw an ordered diagram, interpret its key and use it to find values such as the median, mode and range.

This guide explains each skill step by step, with worked examples and an exam-style question. Stem and leaf diagrams are included explicitly in Pearson Edexcel Foundation content, but requirements vary between exam boards. Check the GCSE Maths topics by exam board and tier to confirm what applies to your course.

What is a stem and leaf diagram?

A stem and leaf diagram displays a set of numbers by splitting each number into two parts. For ordinary two-digit whole numbers:

the stem is usually the tens digit;
the leaf is usually the units digit.

For example, the number $47$ can be written as:

\mid 7

The stem $4$ represents $40$ , while the leaf $7$ represents $7$ . Together they make $47$ .

A stem and leaf diagram is useful because it shows the shape and spread of a data set without losing the individual data values. Unlike a grouped frequency table, you can reconstruct every original number from the diagram.

A typical diagram might look like this:

Stem	Leaf
$1$	$2582\quad5\quad8$
$2$	$1471\quad4\quad7$
$3$	$060\quad6$

Key: $2∣4=242\mid4=24$

The first row represents $12$ , $15$ and $18$ . The next row represents $21$ , $24$ and $27$ .

The key is essential because it explains the place value. Without it, $2∣42\mid4$ could mean $24$ , $2.4$ , $204$ or another value, depending on the context.

How to draw an ordered stem and leaf diagram

An ordered stem and leaf diagram has the leaves arranged from smallest to largest along each row. Ordering the leaves makes it much easier to identify the median, mode, minimum and maximum.

Use these steps:

Identify the smallest and largest values.
Write all the required stems in ascending order.
Split each value into its stem and leaf.
Enter every leaf beside the correct stem.
Arrange the leaves in ascending order within each row.
Count the leaves and compare the total with the number of original values.
Add a clear key with units where appropriate.

Worked example 1: drawing a diagram

The times, in seconds, taken by $12$ students to complete a task are:

23,\ 17,\ 31,\ 25,\ 19,\ 22,\ 27,\ 35,\ 21,\ 18,\ 25,\ 30

The values run from $17$ to $35$ , so the required stems are $1$ , $2$ and $3$ .

Split the numbers into tens and units. For example, $23$ gives stem $2$ and leaf $3$ . After putting every leaf in the correct row, order the leaves from left to right.

Stem	Leaf
$1$	$7897\quad8\quad9$
$2$	$1235571\quad2\quad3\quad5\quad5\quad7$
$3$	$0150\quad1\quad5$

Key: $2∣3=232\mid3=23$ seconds

There are $12$ leaves, matching the $12$ values in the question. The repeated leaf $5$ in the second row must appear twice because the original list contains two values of $25$ .

You can review the same process in the MathsGenie Stem and Leaf lesson and Stem and Leaf revision guide.

How to read information from a stem and leaf diagram

Always begin by reading the key. It tells you how to recombine a stem and leaf and may also state the unit being measured.

To find a particular value, select its stem and leaf and combine them according to the key. If the key is $3∣7=373\mid7=37$ kg, a stem of $4$ with a leaf of $2$ represents $42$ kg.

Finding the range

The range measures the spread of the data. Use:

\text{range}=\text{largest value}-\text{smallest value}

For the diagram in worked example 1, the smallest value is $17$ and the largest is $35$ .

\text{range}=35-17=18

The range is $18$ seconds. A common error is to state the largest value, rather than subtracting the smallest value from it.

Finding the mode

The mode is the value that occurs most often. Repeated leaves represent repeated values.

In worked example 1, $25$ appears twice and every other value appears once. Therefore, the mode is $25$ seconds.

A data set can have more than one mode if several values share the highest frequency. It can also have no mode if every value appears the same number of times.

Finding the median

The median is the middle value when the data is in order. An ordered stem and leaf diagram has already placed the values in ascending order, so you only need to locate the correct position.

For $n$ values, the median position can be found using:

\frac{n+1}{2}

When there are $12$ values, the calculation gives:

\frac{12+1}{2}=6.5

This means the median lies halfway between the $6$ th and $7$ th values. From worked example 1, these are $23$ and $25$ .

\text{median}=\frac{23+25}{2}=24

The median time is $24$ seconds. The answer does not have to be one of the original data values when there is an even number of values.

For more practice with median, mode and range, use the MathsGenie Averages resources.

Stem and leaf diagrams with decimals

The split does not always occur between the tens and units digits. A question may use decimal data, so you must follow the key rather than assuming the place value.

Worked example 2: interpreting decimal data

Consider this diagram showing lengths in centimetres:

Stem	Leaf
$1$	$2582\quad5\quad8$
$2$	$01440\quad1\quad4\quad4$
$3$	$2$

Key: $2∣4=2.42\mid4=2.4$ cm

The data values are:

1.2,\ 1.5,\ 1.8,\ 2.0,\ 2.1,\ 2.4,\ 2.4,\ 3.2

The key shows that the stems represent units and the leaves represent tenths. It would be incorrect to read $2∣42\mid4$ as $24$ .

There are $8$ values, so the median is halfway between the $4$ th and $5$ th values:

\text{median}=\frac{2.0+2.1}{2}=2.05\text{ cm}

The mode is $2.4$ cm because it occurs twice. The range is:

3.2-1.2=2.0\text{ cm}

Completing a partly drawn diagram

Some stem and leaf diagrams exam questions provide an incomplete diagram and the original data list. You must identify which values are missing and place their leaves in the correct positions.

Worked example 3: completing a row

The scores are:

14,\ 17,\ 21,\ 23,\ 26,\ 26,\ 28,\ 31

The partly completed diagram is:

Stem	Leaf
$1$	$474\quad7$
$2$	$13□□81\quad3\quad\square\quad\square\quad8$
$3$	$1$

Key: $2∣1=212\mid1=21$

The missing values in the twenties are both $26$ , so both missing leaves are $6$ .

Stem	Leaf
$2$	$136681\quad3\quad6\quad6\quad8$

Both leaves must be included. Omitting a repeated value changes the number of observations and may also change the mode and median.

Common mistakes in stem and leaf diagrams GCSE Maths questions

Forgetting the key

A diagram without a key does not define its place value. Include a key even if the intended values seem obvious. If units are given, include them in the key.

Leaving the leaves unordered

Unless the question specifically asks for an unordered diagram, arrange each row from smallest to largest. Do not order all leaves as one group because each leaf must remain beside its correct stem.

Missing repeated values

Every observation needs its own leaf. If $32$ appears three times, leaf $2$ must appear three times beside stem $3$ .

Treating the stem as a frequency

The stem is part of each data value, not the number of observations. Frequency is found by counting leaves.

Finding the wrong median position

Count individual leaves, not stems. With an even number of values, identify the two middle values and calculate their mean.

Using the wrong values for the range

Use the complete smallest and largest values. If the key says $4∣2=4.24\mid2=4.2$ , the values are decimals, not $42$ .

Skipping an empty stem

If the data include values in the teens and thirties but none in the twenties, the stem $2$ should usually still be shown with an empty leaf row. This maintains a continuous scale and makes the gap in the data clear.

Foundation exam-style question

The number of pages read by $15$ students is shown below.

18,\ 24,\ 31,\ 27,\ 22,\ 35,\ 19,\ 24,\ 28,\ 32,\ 21,\ 26,\ 24,\ 30,\ 17

(a) Draw an ordered stem and leaf diagram for the data. Include a key. $[3]$

(b) Write down the mode. $[1]$

(c) Work out the median. $[1]$

(d) Work out the range. $[1]$

Answer and marking points

First group the values by their tens digit, then order the units digits.

Stem	Leaf
$1$	$7897\quad8\quad9$
$2$	$124446781\quad2\quad4\quad4\quad4\quad6\quad7\quad8$
$3$	$01250\quad1\quad2\quad5$

Key: $2∣4=242\mid4=24$ pages

For part (a), marks would typically be awarded for placing the leaves on the correct stems, ordering them correctly and giving a valid key. Exact marking arrangements depend on the mark scheme.

For part (b), $24$ occurs three times, so:

\text{mode}=24

For part (c), there are $15$ values. The median is the $8$ th value because:

\frac{15+1}{2}=8

Counting through the ordered diagram, the $8$ th value is $24$ .

\text{median}=24

For part (d), the smallest value is $17$ and the largest is $35$ .

\text{range}=35-17=18

Try 4 more stem and leaf exam questions, then compare your work with the available worked solutions and mark scheme guidance.

A reliable exam method

Before moving to the next question, use this checklist:

read the key before interpreting any value;
write stems in ascending order;
place every leaf beside the correct stem;
order leaves separately within each row;
preserve repeated values;
count the leaves to check none are missing;
include a key and any required units;
use complete data values when finding averages or the range.

If you are asked only to interpret a diagram, you do not need to rewrite the full data set. Counting carefully from the diagram is usually quicker and reduces unnecessary work.

Conclusion

A stem and leaf diagram separates each value into a stem and a leaf while preserving the original data. Foundation questions commonly require you to construct or complete an ordered diagram, use its key and calculate the mode, median or range.

The most important checks are that the leaves are ordered, repeated values are retained and the key states the correct place value. After reviewing the MathsGenie Stem and Leaf topic page, practise under exam conditions and use the worked solutions to correct mistakes.

Sources and referenced URLs