s3 grouped data
4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.
Lesson Overview
Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Learning Objectives
- Explain the key ideas of s3 grouped data
- Apply s3 grouped data to exam-style questions
- Develop independent study skills
- Build cross-topic connections
Prerequisites
- Read the revision notes for s3 grouped data first (GCSE Revise summary)
- Key vocab to pre-teach: Higher Tier Only
- Basic skills: reading the summary notes and answering the practice questions there
Materials & Equipment
- Exercise book, pencil, ruler
- Scientific calculator
- Graph paper and squared paper
- Printed data tables (link below)
Lesson 1: Introduction: s3 grouped data
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Write down everything you already know about s3 grouped data. Then check against the key terms: Higher Tier Only. Use a mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Higher Tier Only.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Before lesson: Read the script below. Pre-teach key vocab: Higher Tier Only.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: s3 grouped data. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Statistics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
Mins 0-5 - Hook: "Today: s3 grouped data. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Statistics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look
Start with the revision notes summary, then attempt: A histogram bar has width 25 and frequency density 3.2. Find the frequency.
Plenary (5 minutes)
Check Out
Your student states one thing they learned and one question they still have about s3 grouped data.
Lesson 2: Core Concepts: s3 grouped data
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from Lesson 1 on s3 grouped data. Check them against the notes below.
Main Content (35 minutes)
Definition: Grouped data organises values into class intervals. When class intervals have different widths, we need special techniques to represent them fairly.
Higher Tier Only: Histograms with unequal class intervals and cumulative frequency graphs are Higher tier topics. You must understand frequency density.
| Item | Detail |
|---|---|
| Class Interval | A range of values grouped together (e.g. 0-10) |
| Frequency | Number of items in each class |
| Frequency Density | Frequency ÷ Class Width |
| Cumulative Frequency | Running total of frequencies |
| Upper Class Boundary | The highest value in a class interval |
| 150-160 | 5 |
| 160-170 | 12 |
| 170-180 | 18 |
Practice (10 minutes)
Q: A histogram bar has width 25 and frequency density 3.2. Find the frequency.
Answer: Frequency = 3.2 × 25 = 80
Plenary (5 minutes)
Explain Back
Your student teaches the key points back to you without looking. Fill any gaps immediately.
Lesson 3: Application: s3 grouped data
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Recall the key terms: Higher Tier Only. Define each in one sentence.
Main Content (35 minutes)
Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.
Q1: A histogram bar has width 25 and frequency density 3.2. Find the frequency.
Answer: Frequency = 3.2 × 25 = 80
Q2: Calculate the frequency density for a class with width 15 and frequency 45.
Answer: Frequency density = 45 ÷ 15 = 3
Q3: A cumulative frequency graph has total 200. What cumulative frequency gives the median?
Answer: Median position = 200 ÷ 2 = 100
Q4: In a histogram, one bar from 0-20 has frequency 50. What is the frequency density?
Answer: Frequency density = 50 ÷ 20 = 2.5
Q5: The cumulative frequencies are: at 40 = 25, at 60 = 70, at 80 = 120. How many values are between 60 and 80?
Answer: 120 - 70 = 50 values between 60 and 80
Plenary (5 minutes)
Error Review
Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.
Lesson 4: Exam Practice: s3 grouped data
Duration: 50 minutes
Starter Activity (5 minutes)
Command Words
Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).
Main Content (35 minutes)
Extended Answer
Extended question: Extended Answer 6 marks: A histogram shows the times taken for 200 runners to complete a race. One bar covers 20–30 minutes with frequency density 4. Another bar covers 30–50 minutes with frequency density 3. (a) Find the frequency for each class. (b) A third class 50–60 minutes has frequency 20. Find its frequency density. (c) Explain why using frequency (not frequency density) on the y-axis would give a misleading histogram. <div class="
(a) 20–30: Frequency = 4 × 10 = 40. 30–50: Frequency = 3 × 20 = 60. (b) 50–60: Width = 10. Frequency density = 20/10 = 2. (c) If frequency were used on the y-axis, the 30–50 class (frequency 60) would have a bar of height 60, and the 20–30 class (frequency 40) would have height 40. But the 30–50 bar would be twice as wide, making its area 1200 vs 400 for 20–30. This visually over-represents the 30–50 group because area is what the eye perceives. Frequency density ensures area = frequency, making visual comparison fair. Mark scheme: M1 for frequency = density × width, A1 for 40 and 60, M1 for density = frequency/width, A1 for 2, M1 for explaining area interpretation, A1 for clear explanation of why frequency alone misleads
Exam Tips: Histograms have NO gaps between bars (continuous data) | For unequal class intervals, always calculate frequency density | Area of bar = frequency (not height!) | Cumulative frequency graphs start at (0, 0) or the lowest boundary | Use the graph to find median, quartiles, and percentiles | Read scales carefully - cumulative frequency graphs have different scales
Common Errors: Watch Out! 1. Wrong: Using frequency as the bar height in a histogram with unequal class intervals Correct: Use frequency density on the y-axis — area of bar = frequency, so height = frequency ÷ class width 2. Wrong: Plotting cumulative frequency at the midpoint of each class interval Correct: Plot cumulative frequency at the UPPER class boundary — cumulative frequency has reached that value by that point 3. Wrong: Using class width of 10 for the interval 10–20 (getting 10 instead of the correct 10, but wrong for intervals like 10–20 where boundaries matter) Correct: Check class boundaries carefully — "10–20" usually means 10 ≤ x
AO3 - Reasoning & Interpretation: Reasoning and Interpretation A cumulative frequency graph for 120 exam scores shows: the curve passes through (40, 0), (50, 15), (60, 48), (70, 85), (80, 108), (90, 118), (100, 120). (a) Use the graph to estimate the median and interquartile range. (b) A score of 65 is needed to pass. Estimate how many students passed. (c) The teacher says "Most students scored between 60 and 80." Use the data to evaluate this claim. Answers: (a) Median at CF=60: read from curve ≈ 64. Q1 at CF=30: ≈ 55. Q3 at CF=90: ≈ 73. IQR = 73−55 = 18. (b) At score 65, read CF ≈ 50. Students passing = 120−50 = 70. (c) Between 60 and 80: CF at 80 = 108, CF at 60 = 48. Students in range = 108−48 = 60 out of 120 = 50%. "Mos
Stretch & Challenge (Grade 8-9):
- Synoptic links: explain how s3 grouped data connects to another Statistics topic you have studied
- Real-world: research one real-world use or example of s3 grouped data
- Critical: "What are the limitations of the models used in s3 grouped data?"
Plenary (5 minutes)
Assessment Criteria
- Got it: Confident explanation + correct worked examples
- Getting there: Main points OK, needs support with detail
- Not yet: Confused on key concepts - re-run Lesson 2
Homework & Consolidation
- Consolidation: Re-answer any Lesson 3 practice questions answered incorrectly (20 mins)
- Retrieval: Write flashcards for the key terms: Higher Tier Only (10 mins)
- Exam practice: One past-paper question on s3 grouped data from the board websites (15 mins)
- Extension: Explain s3 grouped data to someone else in your own words (10 mins)