Year 10 GCSE Maths > Statistics & Probability > Chapter 5

Cumulative frequency diagrams

Higher (Grades 4-9) Non-Calculator Chapter 5/15

What You'll Learn

This chapter covers cumulative frequency diagrams as part of the GCSE Mathematics specification. You'll develop essential skills for Higher tier (Grades 4-9) examination.

Why This Matters for GCSE

Exam Coverage: This topic appears in GCSE non-calculator Paper 1 and calculator Papers 2 & 3. Understanding cumulative frequency diagrams is essential for:

  • Answering direct GCSE exam questions on this topic
  • Problem-solving across multiple mathematics topics
  • Achieving Grades 4-9 on Higher tier papers
  • Building mathematical reasoning and proof skills

GCSE Command Words: "Calculate", "Show that", "Prove", "Explain", "Hence"

Key Concepts

Understanding cumulative frequency diagrams requires mastery of these fundamental concepts:

Key Formula/Method

Apply the appropriate mathematical technique

Follow the step-by-step method shown in examples

Step-by-Step Method

Step 1: Read the question carefully and identify what's being asked
Step 2: Write down the formula or method you'll use
Step 3: Substitute values and calculate step-by-step
Step 4: Check your answer makes sense and write your final answer clearly

Worked Examples

Example 1: Higher Tier Question

Show that: [Question relating to cumulative frequency diagrams]

Identify the given information
Select the appropriate method or formula
Work through the calculation systematically
State the final answer with correct units
Answer: [Complete solution]
Mark Scheme: 1 mark for method, 1 mark for correct working, 1 mark for answer
Example 2: Multi-Step Problem

Problem: A GCSE-style problem involving cumulative frequency diagrams

Break down the problem into manageable steps
Apply the mathematical concepts systematically
Show all working clearly for full marks
Check the answer is reasonable
Answer: [Complete solution with units/context]
Mark Scheme: 2 marks for method, 1 mark for accuracy, 1 mark for final answer (4 marks total)

Practice Questions

Answer these GCSE-style questions. Type your answer and click "Check Answer".

1 [2 marks]

Question 1: [GCSE question on cumulative frequency diagrams]

2 [2 marks]

Question 2: [GCSE question on cumulative frequency diagrams]

3 [3 marks]

Question 3: [Multi-step GCSE question]

4 [2 marks]

Question 4: [GCSE question on cumulative frequency diagrams]

5 [3 marks]

Question 5: [Problem-solving question]

6 [2 marks]

Question 6: [GCSE question on cumulative frequency diagrams]

7 [3 marks]

Question 7: [Application question]

8 [2 marks]

Question 8: [GCSE question on cumulative frequency diagrams]

9 [4 marks]

Question 9: [Complex problem-solving question]

10 [3 marks]

Question 10: [Show that question]

Common GCSE Mistakes

❌ WRONG: Common mistake related to cumulative frequency diagrams
✅ CORRECT: The correct approach and why it works
❌ WRONG: Another typical error students make
✅ CORRECT: The right method with clear explanation
❌ WRONG: Forgetting to show working in 'show that' questions
✅ CORRECT: Always write every step clearly for full marks

GCSE Exam Tips

  • Read carefully: Make sure you understand what the question is asking before you start
  • Show your working: Even if you know the answer, write down the steps for method marks
  • Check units: Always include units in your final answer if the question involves measurements
  • 'Show that' questions: You must prove the given answer by showing complete working
  • Time management: Don't spend too long on one question - move on and come back if needed
  • Check answers: Use the last few minutes to check your answers make sense
  • Grade boundaries: Grade 5 = strong pass, Grade 4 = standard pass - know your target!

Learning Outcomes

By the end of this chapter, you should be able to: