s4 central tendency
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 s4 central tendency
- Apply s4 central tendency to exam-style questions
- Develop independent study skills
- Build cross-topic connections
Prerequisites
- Read the revision notes for s4 central tendency first (GCSE Revise summary)
- Key vocab to pre-teach: key terms from s4 central tendency
- 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: s4 central tendency
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Write down everything you already know about s4 central tendency. Then check against the key terms: key terms from s4 central tendency. 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 s4 central tendency.
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 s4 central tendency.
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: s4 central tendency. 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: s4 central tendency. 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: Find the mean, median, and mode of: 4, 6, 8, 6, 5, 6, 9
Plenary (5 minutes)
Check Out
Your student states one thing they learned and one question they still have about s4 central tendency.
Lesson 2: Core Concepts: s4 central tendency
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from Lesson 1 on s4 central tendency. Check them against the notes below.
Main Content (35 minutes)
Definition: Measures of central tendency identify the "average" or "typical" value in a set of data. The three main measures are mean, median, and mode.
| Term | Meaning | Example |
|---|---|---|
| Mean | Sum of values ÷ number of values | Continuous data, no outliers |
| Median | Middle value when ordered | Data with outliers, skewed data |
| Mode | Most frequent value | Categorical data, identifying most common |
| 2 | 3 | |
| 3 | 5 | |
| 4 | 8 | |
| 5 | 4 | |
| 2 | 3 | 6 |
Practice (10 minutes)
Q: Find the mean, median, and mode of: 4, 6, 8, 6, 5, 6, 9
Answer: Mean = 44÷7 ≈ 6.29; Ordered: 4,5,6,6,6,8,9; Median = 6; Mode = 6
Plenary (5 minutes)
Explain Back
Your student teaches the key points back to you without looking. Fill any gaps immediately.
Lesson 3: Application: s4 central tendency
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Recall the key terms: key terms from s4 central tendency. 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: Find the mean, median, and mode of: 4, 6, 8, 6, 5, 6, 9
Answer: Mean = 44÷7 ≈ 6.29; Ordered: 4,5,6,6,6,8,9; Median = 6; Mode = 6
Q2: The mean of 5 numbers is 12. Four of the numbers are 10, 15, 8, 14. Find the fifth number.
Answer: Total = 5×12 = 60; Fifth = 60 - (10+15+8+14) = 60 - 47 = 13
Q3: Find the range: 23, 45, 12, 67, 34, 89, 56
Answer: Range = 89 - 12 = 77
Q4: A data set has Q1 = 15, Q2 = 28, Q3 = 42. Find the interquartile range.
Answer: IQR = Q3 - Q1 = 42 - 15 = 27
Q5: Which average would you use for favourite colours? Explain why.
Answer: Mode - because colour is categorical data (you cannot calculate mean or median for colours).
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: s4 central tendency
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: Two classes take the same test. Class A: 25 students, mean = 62, range = 35. Class B: 30 students, mean = 58, range = 50. (a) Calculate the combined mean for all 55 students. (b) Compare the performance of the two classes, commenting on both average and spread. (c) A new student joins Class A and scores 95. Explain the effect on the mean and median of Class A. <div class="
(a) Total for A = 25 × 62 = 1550. Total for B = 30 × 58 = 1740. Combined total = 3290. Combined mean = 3290/55 = 59.8 ≈ 60. (b) Class A performed better on average (mean 62 > 58). Class A's results were more consistent (range 35 (c) New mean = (1550+95)/26 = 1645/26 ≈ 63.3 (increased). The new score of 95 is well above the mean, pulling it up. The median will increase slightly because 95 is higher than most scores, shifting the middle value upward, but the change will be much smaller than the change in mean since median is resistant to outliers. Mark scheme: M1 for class totals, A1 for combined mean ≈60, M1 for comparing averages, M1 for comparing spread, A1 for clear comparison statement, M1 for explaining mean increase, A1 for explaining median is less affected
Exam Tips: Always order data before finding the median | Check if there's more than one mode | For grouped data, estimate the mean using midpoints | Use median for data with outliers (less affected by extreme values) | When comparing, comment on both average and spread | Higher tier: Know how to find quartiles and IQR from cumulative frequency graphs
Common Errors: Watch Out! 1. Wrong: Finding the median without ordering the data first Correct: Always arrange data in ascending order before identifying the middle value 2. Wrong: Confusing mean, median and mode — e.g. saying "the most common value is the mean" Correct: Mode = most frequent, Median = middle when ordered, Mean = sum ÷ count — they are different measures 3. Wrong: Using the mean for data with extreme outliers and claiming it represents a "typical" value Correct: For data with outliers (like salaries, house prices), the median better represents a typical value since the mean is pulled towards the outlier
AO3 - Reasoning & Interpretation: Reasoning and Interpretation A company reports: "The mean salary is £42,000. The median salary is £28,000." (a) What does the difference between mean and median tell you about the distribution of salaries? (b) Which average should a journalist use to describe a "typical" salary? Justify your choice. (c) The company removes the CEO's salary of £250,000 and recalculates. Would the mean or median change more? Explain. Answers: (a) Mean > Median indicates right-skewed (positive skew). A few very high salaries pull the mean up above the median. (b) The median (£28,000) — it better represents a typical salary because the mean is inflated by a small number of very high earners. (c) The mean would c
Stretch & Challenge (Grade 8-9):
- Synoptic links: explain how s4 central tendency connects to another Statistics topic you have studied
- Real-world: research one real-world use or example of s4 central tendency
- Critical: "What are the limitations of the models used in s4 central tendency?"
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 s4 central tendency (10 mins)
- Exam practice: One past-paper question on s4 central tendency from the board websites (15 mins)
- Extension: Explain s4 central tendency to someone else in your own words (10 mins)