Quick Summary
📊 Stem & Leaf Diagrams
Split two-digit numbers into tens (stem) and units (leaf). Perfect for displaying ordered data and finding the median quickly.
📈 Bar Charts & Pictograms
Represent discrete data (countable) with bars or symbols. The height shows frequency; the tallest bar is the mode.
🥧 Pie Charts
Circle divided into sectors. Each angle is proportional to frequency. Use 360° = total frequency to solve any problem.
🔍 Reading & Interpreting
Always check the title, axes, keys, and units. Look for trends, use numbers, and consider the scope of the data.
🔗 Comparing Diagrams
Use ranges and statistical measures to compare two data sets. Always relate your findings back to the real-world context.
⚠️ Watch Your Mistakes
Don't write leaf only in medians, don't use protractors on "not to scale" diagrams, and always give context to conclusions.
Stem & Leaf Diagrams
What Is a Stem & Leaf Diagram?
A stem & leaf diagram is a simple way to display an ordered list of data using digits. It works brilliantly when you want to:
- See all values clearly at a glance
- Find the median quickly (it's already ordered)
- Identify any patterns or clusters
How Do They Work?
Two-digit numbers are split into:
- Stem = the tens digit (written vertically, on the left)
- Leaf = the units digit (written horizontally, on the right)
Example: The number 25 is split as 2 | 5
The stem is 2 (representing 20), the leaf is 5 (representing 5 units), so together they make 25.
Worked Example: Blood Pressure Reduction
Question: Draw a stem & leaf diagram for these blood pressure reductions (in mmHg):
12, 31, 24, 18, 21, 34, 40, 19, 23, 17, 16
Step 1: Split each number into stem and leaf:
- 12 → 1|2
- 31 → 3|1
- 24 → 2|4
- 18 → 1|8
- etc.
Step 2: Write the stems down the left (in order), then put the leaves next to each stem in order:
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
Why was this diagram useful? The data is now ordered, so we can instantly see:
- The lowest value is 12, the highest is 40
- Most values are between 16 and 24
- The data is ready for us to find the median
The Key: Always Include Units
The key tells the reader how to interpret the diagram. It's not optional—you must include it.
✓ Correct keys:
- 2|5 means 2.5 degrees
- 2|5 means 2500 people
- 1|8 means 18 years old
Finding the Median from a Stem & Leaf Diagram
The median is the middle value when the data is ordered. Since stem & leaf diagrams are already ordered, this is easy:
- Count the total number of data points
- Find the middle position: if there are 11 values, the median is the 6th value
- Cross out from the beginning and end until you reach the middle
- Write down both the stem AND the leaf
Pie Charts