Statistics Lesson Plan
Mean of Grouped Data - Assumed Mean Method
🎯 Introduction & Hook Activity (8 minutes)
Hook Activity: "The Smart Calculator"
Activity: Present the class with two scenarios:
- Scenario 1: Calculate mean of marks: 52, 48, 55, 51, 49
- Scenario 2: Calculate mean of income data: 25,052, 25,048, 25,055, 25,051, 25,049
Question: "Which one would you prefer to calculate manually? Why?"
Discussion: Lead students to realize that large numbers make calculations tedious and error-prone.
Vocabulary Introduction
- Assumed Mean (A): A convenient value chosen to simplify calculations
- Deviation (di): The difference between class mark and assumed mean
- Class Mark (xi): Mid-point of each class interval
- Frequency (fi): Number of observations in each class
👨🏫 Explicit Teaching/Teacher Modelling - "I Do" (15 minutes)
Concept Introduction
Today we'll learn the Assumed Mean Method - a smart way to calculate mean when dealing with large numbers or to reduce calculation errors.
Where: A = Assumed Mean, di = xi - A, fi = frequency
🔍 Teacher Demonstration Example
Problem: Find the mean marks of 30 students from the frequency table below:
| Class Interval | Frequency (fi) | Class Mark (xi) | di = xi - A | fi × di |
|---|---|---|---|---|
| 10 - 25 | 2 | 17.5 | -32.5 | -65 |
| 25 - 40 | 3 | 32.5 | -17.5 | -52.5 |
| 40 - 55 | 7 | 47.5 | -2.5 | -17.5 |
| 55 - 70 | 6 | 62.5 | 12.5 | 75 |
| 70 - 85 | 6 | 77.5 | 27.5 | 165 |
| 85 - 100 | 6 | 92.5 | 42.5 | 255 |
| Total | 30 | - | - | 360 |
Step-by-Step Solution:
- Choose Assumed Mean (A): A = 62.5 (middle class mark - highlighted in yellow)
- Calculate Class Marks: xi = (Upper limit + Lower limit) / 2
- Find Deviations: di = xi - A
- Calculate fi × di: Multiply frequency by deviation
- Apply Formula:
Mean = A + (Σfidi) / (Σfi)
Mean = 62.5 + (360) / (30)
Mean = 62.5 + 12 = 74.5
Key Teaching Points
- Choose assumed mean strategically (preferably middle value or value with highest frequency)
- Deviations can be positive or negative
- The final result is independent of the assumed mean chosen
- This method reduces calculation errors with large numbers
👥 Group Work - "We Do" (12 minutes)
Group Activity Instructions
Formation: Divide class into groups of 4-5 students
Task: Solve the following problem using assumed mean method
📊 Group Work Problem
Problem: Find the mean weight of 50 students:
| Weight (kg) | Number of Students |
|---|---|
| 30 - 40 | 5 |
| 40 - 50 | 8 |
| 50 - 60 | 15 |
| 60 - 70 | 12 |
| 70 - 80 | 7 |
| 80 - 90 | 3 |
Group Discussion Points:
- Which assumed mean should we choose and why?
- How do we calculate class marks?
- What happens if we choose a different assumed mean?
- Compare your answer with other groups
Teacher's Role During Group Work
- Circulate among groups asking guiding questions
- "Why did you choose this value for A?"
- "What do negative deviations indicate?"
- "How can you verify your answer?"
- Encourage groups to compare different assumed means
✍️ Independent Work - "You Do" (8 minutes)
📝 Individual Practice Problem
Problem: The following table shows the distribution of daily wages of 40 workers:
| Daily Wages (Rs.) | Number of Workers |
|---|---|
| 200 - 300 | 4 |
| 300 - 400 | 8 |
| 400 - 500 | 12 |
| 500 - 600 | 10 |
| 600 - 700 | 6 |
Task: Find the mean daily wage using assumed mean method.
Student Requirements
- Show all steps clearly
- Choose an appropriate assumed mean
- Create a complete frequency table with all columns
- Write a brief reflection: "Why is the assumed mean method helpful?"
🎯 Lesson Closure & Summary (2 minutes)
Key Takeaways
- Assumed mean method simplifies calculations with large numbers
- The choice of assumed mean doesn't affect the final result
- Formula:
Mean = A +ΣfidiΣfi
- Always verify your calculations
📚 Homework Assignment
Problem 1: Consumer Survey Data
A consumer survey recorded the monthly expenditure on groceries for 60 families:
| Monthly Expenditure (Rs.) | Number of Families |
|---|---|
| 1000 - 2000 | 6 |
| 2000 - 3000 | 15 |
| 3000 - 4000 | 20 |
| 4000 - 5000 | 12 |
| 5000 - 6000 | 7 |
Find the mean monthly expenditure using assumed mean method.
Problem 2: Height Distribution
Heights of 100 students are given below:
| Height (cm) | Number of Students |
|---|---|
| 140 - 150 | 8 |
| 150 - 160 | 22 |
| 160 - 170 | 40 |
| 170 - 180 | 25 |
| 180 - 190 | 5 |
Calculate the mean height using two different assumed means and verify that both give the same result.
📋 Assignment Instructions:
- Solve both problems showing complete working
- For Problem 2, use A = 155 and A = 165, compare results
- Write a short note on advantages of assumed mean method
- Submit neat work in your math notebook
- Due Date: Next class period