Stem-and-leaf diagrams (Edexcel GCSE Maths): Revision Notes
Stem-and-leaf diagrams
What is a stem-and-leaf diagram?
A stem-and-leaf diagram is a way of displaying numerical data that keeps all the original values whilst showing them in order of size. This makes it easy to see patterns in the data and calculate statistical measures.
The key advantage of stem-and-leaf diagrams is that they preserve all original data values while organising them visually, unlike other methods like frequency tables that group data into ranges.
The diagram consists of three main parts:
- Stem: represents the tens (or higher place values)
- Leaf: represents the units (ones)
- Key: shows exactly what the stem and leaf values mean
Understanding the structure
In a stem-and-leaf diagram, data is split into two parts. The stem typically represents the tens digit, while the leaf represents the units digit.
Worked Example: Reading a Stem-and-Leaf Value
For the number 27:
- Stem: 2 (representing 20)
- Leaf: 7 (representing 7 units)
- Combined: 27
The key tells you how to read the values. For instance, "Key: 2|7 = 27" means that a stem of 2 and leaf of 7 represents the value 27.
How to draw a stem-and-leaf diagram
Follow these steps to create your own diagram:
- Choose sensible stem values - typically the tens digits of your data
- Draw the stem column in order, then add leaves in any order initially
- Cross off each data value from your original list as you enter it
- Redraw the diagram with leaves arranged in ascending order
- Add a key to show what your notation means
Always remember to arrange the leaves in ascending order in your final diagram. Many students lose marks by leaving leaves in random order after their initial draught.
Finding averages from stem-and-leaf diagrams
Median
The median is the middle value when data is arranged in order. Since stem-and-leaf diagrams already show data in order, finding the median is straightforward.
Critical Point: Always use the complete data value, not just the leaf. For example, if the median leaf is 7 in the stem row 2, the median is 27, not 7.
Mode
The mode is the most frequently occurring value. Look for leaves that appear most often in the same stem row.
Watch Out: Different leaves in different stem rows can represent the same value. For example, leaf 0 in stem row 3 and leaf 10 in stem row 2 both represent 30.
Range
The range is calculated by subtracting the lowest value from the highest value.
Essential Rule: Use the actual data values from the diagram, not just the stem values. Find the complete smallest and largest numbers first.
Worked example analysis
When working with stem-and-leaf diagrams in exams, follow these key strategies:
Exam Success Tips:
- Count the data carefully - the total number of values helps you find the median position
- Read the key properly - this tells you the scale of your data
- Use complete values - never work with just stems or just leaves when calculating statistics
- Show your working - especially when finding medians, as you may need to identify the middle position
Common exam mistakes to avoid
Critical Mistakes to Avoid:
- Forgetting to use the key when reading values
- Using stem values instead of complete data values for calculations
- Not arranging leaves in order when drawing diagrams
- Miscounting the total number of data values
- Confusing the range calculation by using stems only
Summary
Key Points to Remember:
- Stem-and-leaf diagrams display data in order whilst preserving original values
- Always read the key to understand what the numbers represent
- Use complete data values (stem + leaf) for all calculations, never just the leaf
- The median is easy to find as data is already ordered
- Count carefully when identifying the middle value for median calculations