Stem & Leaf Diagrams (Cambridge International IGCSE Maths)

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

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 2500 people

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

Exam Hint 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.

Answer:

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

Final answer:	Final answer: **Blood pressure reduction
Final answer: 1	Final answer:** 2 6 7 8 9 **
Final answer: 2	Final answer:** 1 3 4 **
Final answer: 3	Final answer:** 1 4 **
Final answer: 4	Final answer:** 0

Final answer: 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.

Answer:

Find the middle value This is the 6th patient

* *	* Blood pressure reduction
1	2 6 7 8 9
2	$\text circled{1}$ 3 4
3	1 4
4	0

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

Final answer: The median is 21 mmHg