ST10: Charts & Diagrams
Learn how to construct and interpret pictograms, pie charts, stem-and-leaf diagrams, Venn diagrams, and population pyramids for GCSE Statistics.
Charts & Diagrams
Learn how to construct and interpret pictograms, pie charts, stem-and-leaf diagrams, Venn diagrams, and population pyramids for GCSE Statistics.
Key Fact: A pictogram uses symbols or pictures to represent data; each symbol represents a fixed quantity stated in the key.
Key Fact: In a pie chart, the angle of each sector is proportional to the frequency it represents: angle = (frequency ÷ total) × 360°.
Key Fact: To construct a pie chart, calculate each sector angle, draw a circle, and use a protractor to measure each angle from the previous sector.
Key Fact: A stem-and-leaf diagram displays data in order while retaining the original values; the stem shows the leading digits and the leaf shows the final digit.
Key Fact: In a stem-and-leaf diagram, leaves must be ordered from smallest to largest and a key must be provided (e.g. 3 | 7 means 37).
Key Fact: A back-to-back stem-and-leaf diagram compares two datasets using the same stem, with leaves of one dataset on each side.
Key Fact: A Venn diagram uses overlapping circles to show the relationships between sets; the overlapping region represents elements common to both sets.
Key Fact: The union of sets A and B (A ∪ B) includes all elements in A or B or both; the intersection (A ∩ B) includes only elements in both.
Key Fact: A population pyramid is a paired bar chart showing the age and sex distribution of a population, with males on the left and females on the right.
Key Fact: Population pyramids allow comparison of demographic structure; a wide base indicates a high birth rate, while a narrow base indicates a low birth rate.
Key Fact: When interpreting pictograms, check the key carefully — a half symbol represents half the stated quantity, and a quarter symbol a quarter.
Key Fact: Pie charts show the proportion of each category relative to the whole but do not show actual frequencies unless labelled.
📋 Key Vocabulary and Concepts
For Charts & Diagrams, you must know:
- Pictogram: A chart that uses symbols or pictures to represent data, where each symbol represents a fixed quantity given in the key.
- Pie chart: A circular chart divided into sectors, where the angle of each sector is proportional to the frequency of the category.
- Stem-and-leaf diagram: A diagram that displays ordered data by splitting each value into a stem (leading digits) and a leaf (final digit), preserving the original data.
- Venn diagram: A diagram using overlapping circles to show the relationships between sets, including intersection and union.
- Population pyramid: A paired bar chart showing the age–sex structure of a population, with males on the left and females on the right of a central axis.
- Sector: A slice of a pie chart representing a category; its angle is proportional to the category's frequency.
❓ Practice Questions
Q: In a pie chart, a category has frequency 15 out of a total of 60. What angle should its sector have?
Q: A stem-and-leaf diagram has stem 4 and leaves 2, 5, 7, 8. What are the actual data values if the key is 4 | 2 means 42?
Q: In a Venn diagram, set A has 20 elements, set B has 15 elements, and A ∩ B has 8 elements. How many elements are in A ∪ B?
Q: A pictogram uses one circle to represent 10 cars. How many circles represent 35 cars?
Q: What does a wide base on a population pyramid indicate?
✅ Answers
- Angle = (15 ÷ 60) × 360° = 0.25 × 360° = 90°.
- The data values are 42, 45, 47, and 48.
- A ∪ B = 20 + 15 – 8 = 27 elements.
- 3 whole circles and one half circle, since 35 ÷ 10 = 3.5.
- A wide base indicates a high birth rate, meaning a large proportion of the population is in the youngest age groups.
🎯 Exam Tips
- Always include a key on stem-and-leaf diagrams and pictograms — you will lose marks without one.
- When drawing pie charts, always label each sector with the category name and preferably the percentage or frequency.
- In a Venn diagram, the region outside both circles represents elements that are in neither set — do not forget this in probability questions.
- When comparing two datasets using a back-to-back stem-and-leaf, comment on the shape, median, and spread.
- Population pyramids can show ageing populations (narrow base, wide top) or young populations (wide base, narrow top) — use these terms in your comparisons.
📝 Exam Technique
GCSE Statistics Exam Tips — Charts & Diagrams:
1. For Charts & Diagrams questions, show every step of your working clearly — method marks count even if the final answer is wrong
2. Check your answer makes sense in context (estimation, units, reasonableness)
3. Use correct mathematical notation and state formulae before substituting values
4. If a Charts & Diagrams question asks you to 'prove' or 'show', write a logical chain of reasoning with a conclusion line
5. For problem-solving, identify the topic first, then recall the relevant method
1. For Charts & Diagrams questions, show every step of your working clearly — method marks count even if the final answer is wrong
2. Check your answer makes sense in context (estimation, units, reasonableness)
3. Use correct mathematical notation and state formulae before substituting values
4. If a Charts & Diagrams question asks you to 'prove' or 'show', write a logical chain of reasoning with a conclusion line
5. For problem-solving, identify the topic first, then recall the relevant method
⚠️ Common Errors
✗ Forgetting to include a key on a stem-and-leaf diagram or pictogram ✓ Always write a key, e.g. '3 | 7 means 37' for stem-and-leaf, or use a symbol key for pictograms.
✗ Calculating pie chart angles using percentages instead of frequencies ✓ Angle = (frequency ÷ total frequency) × 360°; percentages can be used but must total 100% and the formula becomes (percentage ÷ 100) × 360°.
✗ Not ordering leaves in a stem-and-leaf diagram ✓ Leaves must be arranged in ascending order from the stem; unordered leaves lose marks and make it harder to find the median.
✗ Confusing union and intersection in Venn diagrams ✓ Union (A ∪ B) is all elements in A or B or both; intersection (A ∩ B) is only elements in both A and B simultaneously.
✍️ Model Answer
Full-Mark Response
The table shows the number of students in each year group at a school. Draw a pie chart to represent the data. Year 7: 130, Year 8: 120, Year 9: 110, Year 10: 100, Year 11: 90
Total = 130 + 120 + 110 + 100 + 90 = 550 Year 7: (130 ÷ 550) × 360° = 85.1° Year 8: (120 ÷ 550) × 360° = 78.5° Year 9: (110 ÷ 550) × 360° = 72.0° Year 10: (100 ÷ 550) × 360° = 65.5° Year 11: (90 ÷ 550) × 360° = 58.9° Check: 85.1 + 78.5 + 72.0 + 65.5 + 58.9 = 360.0° Draw a circle, draw a radius, then measure each angle in order using a protractor. Label each sector with the year group and angle.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Knowledge & Understanding): Demonstrate knowledge and understanding of charts & diagrams, including data collection, presentation and calculation techniques relevant to Edexcel 1ST0 & AQA 8382.
AO2 (Application): Apply knowledge and understanding of charts & diagrams to interpret data, reason statistically and draw conclusions in context.
AO3 (Evaluation): Evaluate statistical methods and conclusions, assessing appropriateness, reliability, validity and bias through the statistical enquiry cycle.
📝 Exam Questions by Topic
- AQA Past Papers - Topic Questions -- AQA
- Edexcel Past Papers - Topic Questions -- Edexcel
- CCEA Past Papers - Topic Questions -- CCEA
🎬 Video Resources
Ready to ace your GCSE Statistics exams?
Get the best revision books and guides to boost your grades.