measures spread
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 measures spread
- Apply measures spread to exam-style questions
- Develop independent study skills
- Build cross-topic connections
Prerequisites
- Read the revision notes for measures spread first (GCSE Revise summary)
- Key vocab to pre-teach: key terms from measures spread
- 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: measures spread
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Write down everything you already know about measures spread. Then check against the key terms: key terms from measures spread. Use a mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: key terms from measures spread.
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: key terms from measures spread.
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: measures spread. 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: measures spread. 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: explain the key ideas of measures spread
Plenary (5 minutes)
Check Out
Your student states one thing they learned and one question they still have about measures spread.
Lesson 2: Core Concepts: measures spread
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from Lesson 1 on measures spread. Check them against the notes below.
Main Content (35 minutes)
Key Fact: The range is the difference between the largest and smallest values: range = maximum – minimum; it is affected by outliers.
Key Fact: The interquartile range (IQR) = Q3 – Q1; it measures the spread of the middle 50% of the data and is not affected by outliers.
Key Fact: The IQR is preferred over the range when the data contains outliers or is skewed, because it ignores extreme values.
Key Fact: The pth percentile is the value below which p% of the data falls; it can be read from a cumulative frequency curve.
Key Fact: The 10th percentile (P10) is the value at 10% of the total cumulative frequency; the 90th percentile (P90) is at 90%.
Key Fact: The interpercentile range is the difference between two percentiles, e.g. P90 – P10, which captures the middle 80% of the data.
Practice (10 minutes)
Q: explain the key ideas of measures spread
Answer:
Plenary (5 minutes)
Explain Back
Your student teaches the key points back to you without looking. Fill any gaps immediately.
Lesson 3: Application: measures spread
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Recall the key terms: key terms from measures spread. 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.
Work through the practice questions on the revision notes page for this topic.
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: measures spread
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: Full-Mark Response Calculate the standard deviation of the following sample data: 4, 7, 8, 10, 11. <div class="
Step 1: Find the mean. x̄ = (4 + 7 + 8 + 10 + 11) ÷ 5 = 40 ÷ 5 = 8 Step 2: Calculate deviations from the mean and square them: x | x – x̄ | (x – x̄)² 4 | –4 | 16 7 | –1 | 1 8 | 0 | 0 10| 2 | 4 11| 3 | 9 Sum | 30 Step 3: Variance = Σ(x – x̄)² ÷ (n – 1) = 30 ÷ 4 = 7.5 Step 4: Standard deviation = √7.5 ≈ 2.74 (to 2 d.p.)
Exam Tips: When calculating standard deviation, show each step: find the mean, calculate deviations, square them, sum, divide, and square root. | Use (n – 1) as the divisor for sample standard deviation; use n for population standard deviation — check which the question specifies. | When reading percentiles from a cumulative frequency curve, use a ruler for accuracy and show dotted lines from the y-axis to the curve and down to the x-axis. | Always state which measure of spread you are using and why — e.g. 'I prefer the IQR because the data contains outliers'. | In comparison questions, write full sentences: 'The IQR for group A (12) is smaller than the IQR for group B (18), so group A's data is less s
Common Errors: ✗ Using n instead of (n – 1) when calculating sample standard deviation ✓ For a sample, divide by (n – 1) to get an unbiased estimate; dividing by n underestimates the true standard deviation of the population. ✗ Calculating range as maximum value minus minimum value including outliers without comment ✓ The range is heavily affected by outliers; if outliers exist, use the IQR or interpercentile range instead, or state that the range is unreliable. ✗ Forgetting to square root the variance to get the standard deviation ✓ Standard deviation = √variance; if variance is 49, then SD = 7, not 49. ✗ Confusing percentile position with percentile value ✓ The 25th percentile position is at 25% of the t
Stretch & Challenge (Grade 8-9):
- Synoptic links: explain how measures spread connects to another Statistics topic you have studied
- Real-world: research one real-world use or example of measures spread
- Critical: "What are the limitations of the models used in measures spread?"
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: key terms from measures spread (10 mins)
- Exam practice: One past-paper question on measures spread from the board websites (15 mins)
- Extension: Explain measures spread to someone else in your own words (10 mins)