Stem & Leaf Diagrams

What is a stem-and-leaf diagram?

A stem-and-leaf diagram is a simple way to display an ordered list of data using digits
Two-digit numbers are split into a tens digit (the stem) and a units digit (the leaf)
- 25 becomes 2 | 5
- The stem is written vertically and the leaves are written horizontally (in order)
The following diagram shows the ages below
- 11, 18, 20, 21, 25, 28, 29, 35, 36, 40

	Age
1	1 8
2	0 1 5 8 9
3	5 6
4	0

Key: 1|8 means 18 years old

What is the key on a stem-and-leaf diagram?

The key shows how values are formed from digits
- It should include units
Other keys are possible
- 2 | 5 represents 2.5 degrees
- 2 | 5 represents 2005 people

What is a back to back stem and leaf diagram?

Occasionally you may encounter a back to back stem and leaf diagram
These display two series of data, both using the same variable, on one diagram
- For example, the number of ice-creams sold each day, for 10 particular days in August compared to September
  - Pay close attention to the key
  - Note that the leaves on the left increase from the centre outwards

Ice creams sold each day in August		Ice creams sold each day in September
	0	1 8
5 3	1	0 1 5 8 9
9 7 2	2	5 6
9 7 6 5 2	3	0

Key: 2|1|8 represents 12 ice creams sold on a day in August, and 18 sold on a day in September

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

The median is the middle number
- Data values are already in order
- You can cross out numbers from the beginning and end until they meet in the middle
  - Remember that the highest number will be at the end of the last stem
  - If two numbers remain in the middle, find the midpoint between them

Examiner Tip

A common mistake when finding the median is to write down the leaf only (median = 6) rather than the stem and leaf (median = 26).

Worked example

A hospital is investigating a new drug that claims to reduce blood pressure.
The reductions in blood pressure, measured in mmHG (millimetres of mercury), for 11 patients are shown below.

12 31 24 18 21 34 40 19 23 17 16

(a)

Draw a stem and leaf diagram to show these results.

Split each value into its tens digit (stem) and units digit (leaf)
The values are not yet in order

	Blood pressure reduction
1	2 8 9 7 6
2	4 1 3
3	1 4
4	0

Put the values in order
Write down the key

	Blood pressure reduction
1	2 6 7 8 9
2	1 3 4
3	1 4
4	0

Key: 1|2 means a blood pressure reduction of 12 mmHG

(b)

Use your stem and leaf diagram to find the median blood pressure reduction.

Find the middle value
This is the 6th patient

	Blood pressure reduction
1	2 6 7 8 9
2	$1$ 3 4
3	1 4
4	0

The median has a leaf of 1 and a stem of 2

The median is 21 mmHG

Stem & Leaf Diagrams (Edexcel GCSE Maths: Foundation)

Revision Note