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skewness & outliers

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: skewness & outliers

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about skewness & outliers. Then check against the key terms: key terms from skewness & outliers. 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 skewness & outliers.
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: skewness & outliers. 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 skewness & outliers

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about skewness & outliers.

Lesson 2: Core Concepts: skewness & outliers

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on skewness & outliers. Check them against the notes below.

Main Content (35 minutes)

Key Fact: A symmetric distribution has its mean, median, and mode approximately equal; the left and right sides are mirror images.
Key Fact: Positive (right) skew has a long tail to the right; the mean is greater than the median, which is greater than the mode.
Key Fact: Negative (left) skew has a long tail to the left; the mean is less than the median, which is less than the mode.
Key Fact: Pearson's skewness coefficient = 3 × (mean – median) ÷ standard deviation; a positive value indicates positive skew, a negative value indicates negative skew.
Key Fact: Values of Pearson's skewness coefficient between –0.5 and 0.5 suggest approximately symmetric data; values beyond ±1 indicate substantial skew.
Key Fact: On a box plot, positive skew is shown by a longer right whisker and the median closer to Q1; negative skew by a longer left whisker and the median closer to Q3.

Practice (10 minutes)

Q: explain the key ideas of skewness & outliers

Answer:

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: skewness & outliers

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: key terms from skewness & outliers. 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: skewness & outliers

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 A dataset of 10 test scores has Q1 = 35, Q2 = 52, Q3 = 65, mean = 54, and SD = 18. The maximum value is 110. Determine whether the maximum is an outlier and calculate Pearson's skewness coefficient. <div class="

Outlier test using 1.5 × IQR: IQR = 65 – 35 = 30 Upper boundary = 65 + 1.5 × 30 = 65 + 45 = 110 Since 110 equals (not exceeds) the boundary, it is not classified as an outlier by the 1.5 × IQR rule. It is at the very edge. Pearson's skewness coefficient: Skewness = 3 × (mean – median) ÷ SD = 3 × (54 – 52) ÷ 18 = 6 ÷ 18 = 0.333 Since 0.333 is between –0.5 and 0.5, the distribution is approximately symmetric with a very slight positive skew.

Exam Tips: When describing skewness, always state the direction (positive/negative) and support it with evidence from mean vs median or from the box plot shape. | Show full working when using the 1.5 × IQR rule: calculate IQR, find the boundaries, then compare each suspected outlier to the boundaries. | When an outlier is found, always comment on whether it should be included or excluded and give a reason (e.g. 'it may be a recording error' or 'it is a genuine extreme value'). | Pearson's skewness coefficient requires the standard deviation; if not given, you can still describe skewness qualitatively by comparing mean and median. | Remember that the 2 SD rule assumes the data is approximately normally
Common Errors: ✗ Saying a distribution is skewed just because it is not perfectly symmetric ✓ Small deviations from symmetry are normal; only describe a distribution as skewed when the asymmetry is clearly visible or the skewness coefficient is substantial. ✗ Confusing the direction of skew ✓ In positive skew, the tail goes to the RIGHT (towards higher values) and the mean is above the median. In negative skew, the tail goes to the LEFT and the mean is below the median. ✗ Forgetting to check whether an outlier is a data error before deciding to remove it ✓ Always investigate outliers first; if a value is a genuine measurement, it should not be removed without justification. Only remove values confirmed as
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how skewness &amp; outliers connects to another Statistics topic you have studied
  • Real-world: research one real-world use or example of skewness &amp; outliers
  • Critical: "What are the limitations of the models used in skewness &amp; outliers?"

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

Recommended Resources

🎓 Smart Lesson (Guided)