ST2: Measures Of 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, CCEA
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, CCEA
Learning Objectives
- Master core concepts of measures of spread
- Apply to exam questions confidently
- Develop independent study skills
- Build cross-topic connections
Prerequisites
- Review ST1 measures of central tendency
- Key vocab: key vocabulary for st2
- Basic skills: basic literacy and numeracy
Materials & Equipment
- Exercise book, coloured pens
- Scientific calculator
- Ruler, protractor, compass (if needed)
- Printed spec/textbook reference
- Internet for videos (see Resources)
Lesson 1: Introduction: Measures Of Spread
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
3 quick questions to activate prior knowledge about measures of spread. Use mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: Measures Of Spread.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: Measures Of Spread.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Measures Of Spread. Goal: by the end you can ✗ 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 p, using the method shown step by step. Connects to the previous lesson in this unit because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Measures Of Spread is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like ✗ 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 p - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Mins 0-5 - Hook: "Today: Measures Of Spread. Goal: by the end you can ✗ 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 p, using the method shown step by step. Connects to the previous lesson in this unit because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Measures Of Spread is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like ✗ 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 p - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic
Q: ✗ 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 p
- What is asked? Explain
- Recall knowledge:
- Apply: ✗ 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.
- Check: Check the units named in the question and sense-check the size of your answer.
- Answer: 7, not 49
Tip: "Show working - method marks > answer marks."
Worked Example 2: Multi-step
Q: ✗ 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 p
- Break down: Separate parts?
- Solve each: ✗ 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 standar
- Combine: The parts chain: each answer feeds the next step of the question.
- Final answer: Evidence cited from the lesson content.
Worked Example 3: Data/Application
Q: ✗ 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 p
- Read data: Axes, units, scale
- Patterns: Trends, anomalies
- Explain: Why? Using measures of spread
- Conclude: Evidence-based
Common Questions & Troubleshooting
Q: "Why does Measures Of Spread work this way?"
A: Analogy: "✗ 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 p". Try re-draw or re-write the worked example from memory, then check it against the model answer.
A: Analogy: "✗ 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 p". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.
Assessment & Model Answers
Mastery Checklist:
- [ ] Define Measures Of Spread in own words
- [ ] Identify features in diagram
- [ ] Explain process step-by-step
- [ ] Apply to unfamiliar context
- [ ] Score 80%+ on past paper question
Model Answer: Past Paper Question
Q: ✗ 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 p
- 1 mark: [Key terminology]
- 1 mark: [Mechanism/process]
- 1 mark: [Application/example]
- 1 mark: [Evaluation - Higher]
Model response: "[Complete answer with expected detail/terminology]"
Why full marks: [What makes this strong]
Stretch & Challenge (Grade 8-9):
- Synoptic links: Connect to ST1-measures-of-central-tendency / ST3-correlation-and-regression
- Real-world: Research use in industry, medicine or research
- Advanced calc: Try a more challenging variant
- Critical: "Evaluate limitations of today's model"
- Research: Recent discovery on measures of spread, summarise 100 words
Plenary (5 mins)
Label the Diagram
Unlabelled diagram - write all parts in 1 min
Assessment Criteria
- Got it: Confident explanation + correct worked examples
- Getting there: Main points OK, needs support with detail
- Not yet: Confused on key concepts, needs reteaching
Lesson 2: Core Concepts: Measures Of Spread
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from last lesson on measures of spread. Use mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: Measures Of Spread.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: Measures Of Spread.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Measures Of Spread. Goal: by the end you can ✗ 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 p, using the method shown step by step. Connects to the previous lesson in this unit because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Measures Of Spread is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like ✗ 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 p - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Mins 0-5 - Hook: "Today: Measures Of Spread. Goal: by the end you can ✗ 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 p, using the method shown step by step. Connects to the previous lesson in this unit because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Measures Of Spread is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like ✗ 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 p - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic
Q: ✗ 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 p
- What is asked? Explain
- Recall knowledge:
- Apply: ✗ 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.
- Check: Check the units named in the question and sense-check the size of your answer.
- Answer: 7, not 49
Tip: "Show working - method marks > answer marks."
Worked Example 2: Multi-step
Q: ✗ 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 p
- Break down: Separate parts?
- Solve each: ✗ 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 standar
- Combine: The parts chain: each answer feeds the next step of the question.
- Final answer: Evidence cited from the lesson content.
Worked Example 3: Data/Application
Q: ✗ 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 p
- Read data: Axes, units, scale
- Patterns: Trends, anomalies
- Explain: Why? Using measures of spread
- Conclude: Evidence-based
Common Questions & Troubleshooting
Q: "Why does Measures Of Spread work this way?"
A: Analogy: "✗ 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 p". Try re-draw or re-write the worked example from memory, then check it against the model answer.
A: Analogy: "✗ 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 p". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.
Assessment & Model Answers
Mastery Checklist:
- [ ] Define Measures Of Spread in own words
- [ ] Identify features in diagram
- [ ] Explain process step-by-step
- [ ] Apply to unfamiliar context
- [ ] Score 80%+ on past paper question
Model Answer: Past Paper Question
Q: ✗ 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 p
- 1 mark: [Key terminology]
- 1 mark: [Mechanism/process]
- 1 mark: [Application/example]
- 1 mark: [Evaluation - Higher]
Model response: "[Complete answer with expected detail/terminology]"
Why full marks: [What makes this strong]
Stretch & Challenge (Grade 8-9):
- Synoptic links: Connect to ST1-measures-of-central-tendency / ST3-correlation-and-regression
- Real-world: Research use in industry, medicine or research
- Advanced calc: Try a more challenging variant
- Critical: "Evaluate limitations of today's model"
- Research: Recent discovery on measures of spread, summarise 100 words
Plenary (5 mins)
Label the Diagram
Unlabelled diagram - write all parts in 1 min
Assessment Criteria
- Got it: Confident explanation + correct worked examples
- Getting there: Main points OK, needs support with detail
- Not yet: Confused on key concepts, needs reteaching
Lesson 3: Application: Measures Of Spread
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from last lesson on measures of spread. Use mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: Measures Of Spread.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: Measures Of Spread.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Measures Of Spread. Goal: by the end you can ✗ 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 p, using the method shown step by step. Connects to the previous lesson in this unit because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Measures Of Spread is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like ✗ 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 p - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Mins 0-5 - Hook: "Today: Measures Of Spread. Goal: by the end you can ✗ 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 p, using the method shown step by step. Connects to the previous lesson in this unit because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Measures Of Spread is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like ✗ 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 p - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic
Q: ✗ 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 p
- What is asked? Explain
- Recall knowledge:
- Apply: ✗ 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.
- Check: Check the units named in the question and sense-check the size of your answer.
- Answer: 7, not 49
Tip: "Show working - method marks > answer marks."
Worked Example 2: Multi-step
Q: ✗ 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 p
- Break down: Separate parts?
- Solve each: ✗ 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 standar
- Combine: The parts chain: each answer feeds the next step of the question.
- Final answer: Evidence cited from the lesson content.
Worked Example 3: Data/Application
Q: ✗ 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 p
- Read data: Axes, units, scale
- Patterns: Trends, anomalies
- Explain: Why? Using measures of spread
- Conclude: Evidence-based
Common Questions & Troubleshooting
Q: "Why does Measures Of Spread work this way?"
A: Analogy: "✗ 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 p". Try re-draw or re-write the worked example from memory, then check it against the model answer.
A: Analogy: "✗ 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 p". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.
Assessment & Model Answers
Mastery Checklist:
- [ ] Define Measures Of Spread in own words
- [ ] Identify features in diagram
- [ ] Explain process step-by-step
- [ ] Apply to unfamiliar context
- [ ] Score 80%+ on past paper question
Model Answer: Past Paper Question
Q: ✗ 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 p
- 1 mark: [Key terminology]
- 1 mark: [Mechanism/process]
- 1 mark: [Application/example]
- 1 mark: [Evaluation - Higher]
Model response: "[Complete answer with expected detail/terminology]"
Why full marks: [What makes this strong]
Stretch & Challenge (Grade 8-9):
- Synoptic links: Connect to ST1-measures-of-central-tendency / ST3-correlation-and-regression
- Real-world: Research use in industry, medicine or research
- Advanced calc: Try a more challenging variant
- Critical: "Evaluate limitations of today's model"
- Research: Recent discovery on measures of spread, summarise 100 words
Plenary (5 mins)
Exam Question Speed Round
5 quick questions, 1 min each. Mark together.
Assessment Criteria
- Got it: Confident explanation + correct worked examples
- Getting there: Main points OK, needs support with detail
- Not yet: Confused on key concepts, needs reteaching
Lesson 4: Exam Practice: Measures Of Spread
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from last lesson on measures of spread. Use mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: Measures Of Spread.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: Measures Of Spread.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Measures Of Spread. Goal: by the end you can ✗ 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 p, using the method shown step by step. Connects to the previous lesson in this unit because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Measures Of Spread is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like ✗ 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 p - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Mins 0-5 - Hook: "Today: Measures Of Spread. Goal: by the end you can ✗ 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 p, using the method shown step by step. Connects to the previous lesson in this unit because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Measures Of Spread is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like ✗ 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 p - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic
Q: ✗ 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 p
- What is asked? Explain
- Recall knowledge:
- Apply: ✗ 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.
- Check: Check the units named in the question and sense-check the size of your answer.
- Answer: 7, not 49
Tip: "Show working - method marks > answer marks."
Worked Example 2: Multi-step
Q: ✗ 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 p
- Break down: Separate parts?
- Solve each: ✗ 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 standar
- Combine: The parts chain: each answer feeds the next step of the question.
- Final answer: Evidence cited from the lesson content.
Worked Example 3: Data/Application
Q: ✗ 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 p
- Read data: Axes, units, scale
- Patterns: Trends, anomalies
- Explain: Why? Using measures of spread
- Conclude: Evidence-based
Common Questions & Troubleshooting
Q: "Why does Measures Of Spread work this way?"
A: Analogy: "✗ 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 p". Try re-draw or re-write the worked example from memory, then check it against the model answer.
A: Analogy: "✗ 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 p". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.
Assessment & Model Answers
Mastery Checklist:
- [ ] Define Measures Of Spread in own words
- [ ] Identify features in diagram
- [ ] Explain process step-by-step
- [ ] Apply to unfamiliar context
- [ ] Score 80%+ on past paper question
Model Answer: Past Paper Question
Q: ✗ 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 p
- 1 mark: [Key terminology]
- 1 mark: [Mechanism/process]
- 1 mark: [Application/example]
- 1 mark: [Evaluation - Higher]
Model response: "[Complete answer with expected detail/terminology]"
Why full marks: [What makes this strong]
Stretch & Challenge (Grade 8-9):
- Synoptic links: Connect to ST1-measures-of-central-tendency / ST3-correlation-and-regression
- Real-world: Research use in industry, medicine or research
- Advanced calc: Try a more challenging variant
- Critical: "Evaluate limitations of today's model"
- Research: Recent discovery on measures of spread, summarise 100 words
Plenary (5 mins)
Exam Question Speed Round
5 quick questions, 1 min each. Mark together.
Assessment Criteria
- Got it: Confident explanation + correct worked examples
- Getting there: Main points OK, needs support with detail
- Not yet: Confused on key concepts, needs reteaching
📝 Mark Scheme Guidance
How examiners mark ST2: Read the command word carefully — State = one word/phrase (1 mark), Describe = pattern or detail (2 marks), Explain = reason with "because" (2–3 marks), Compare = similarities AND differences, Evaluate = both sides + conclusion. Method marks are awarded for correct working even if the final answer is wrong. Always show your working — unexplained answers score zero for AO2.
Success on ST2 questions: Underline the command word, count the marks (one mark per point expected), and answer in the format the command word demands.
Board Notes & Revision Links
This lesson is examined by: AQA 8382 | Edexcel 1ST0 | CCEA units. Tier and paper details vary - always check your board's current specification.
Follow-up revision: measures-spread on GCSE Revise (notes, flashcards and auto-graded target tests for this exact topic).
Homework & Consolidation
- Consolidation: Textbook end-of-topic questions (30 mins)
- Retrieval: 10 flashcards for key terms (15 mins)
- Exam practice: 2 past paper questions (20 mins)
- Extension: Research real-world application (optional, 30 mins)