📊 Statistics Grade 10
Mean of Grouped Data - Direct Method
Complete Interactive Lesson Plan
Hook Activity: "Guess the Average Height"
5 minutesLet's start with an engaging challenge! Look at this frequency table showing height ranges of students in a fictional classroom. Can you estimate what the average height might be?
| Height Range (cm) | Number of Students |
|---|---|
| 150-154 | 3 |
| 155-159 | 8 |
| 160-164 | 12 |
| 165-169 | 5 |
| 170-174 | 2 |
🤔 Think about it: What's your guess for the average height? Write it down! By the end of this lesson, you'll know exactly how to calculate the precise answer.
Essential Vocabulary
3 minutesBefore we dive in, let's understand the key terms we'll be using:
Data organized into class intervals or ranges (like 150-154 cm)
A range of values that groups similar data points together
The number of observations that fall within each class interval
The middle value of each class interval, calculated as (lower limit + upper limit) ÷ 2
A method for calculating mean using the formula: Mean = Σ(f × x)Σf
Teacher Modeling (I Do)
15 minutesA teacher recorded test scores of 30 students in grouped form. Let's find the mean score step by step:
| Score Range | Frequency (f) |
|---|---|
| 60-69 | 4 |
| 70-79 | 8 |
| 80-89 | 12 |
| 90-99 | 6 |
Find the class mark (x) for each interval:
- 60-69: x = (60 + 69) ÷ 2 = 64.5
- 70-79: x = (70 + 79) ÷ 2 = 74.5
- 80-89: x = (80 + 89) ÷ 2 = 84.5
- 90-99: x = (90 + 99) ÷ 2 = 94.5
Create the calculation table:
| Score Range | Frequency (f) | Class Mark (x) | f × x |
|---|---|---|---|
| 60-69 | 4 | 64.5 | 258 |
| 70-79 | 8 | 74.5 | 596 |
| 80-89 | 12 | 84.5 | 1014 |
| 90-99 | 6 | 94.5 | 567 |
| Total | 30 | - | 2435 |
Apply the direct method formula:
✅ Result: The average test score is approximately 81.17 marks.
This means that on average, students scored about 81 marks out of 100.
Group Work (We Do)
12 minutesInstructions: Work in groups of 4-5 students to solve this real-world problem.
A survey of 40 families recorded their monthly grocery expenses. Calculate the mean monthly expense:
| Expense Range (₹) | Number of Families |
|---|---|
| 2000-2999 | 5 |
| 3000-3999 | 12 |
| 4000-4999 | 15 |
| 5000-5999 | 6 |
| 6000-6999 | 2 |
Use this calculator to verify your calculations:
Independent Work (You Do)
8 minutesCalculate the mean age of 25 people at a community center:
| Age Group | Frequency |
|---|---|
| 20-29 | 6 |
| 30-39 | 10 |
| 40-49 | 7 |
| 50-59 | 2 |
Your task: Find the mean age using the direct method.
Find the mean daily wage of 50 workers in a factory:
| Wage Range (₹) | Number of Workers |
|---|---|
| 200-299 | 8 |
| 300-399 | 15 |
| 400-499 | 18 |
| 500-599 | 7 |
| 600-699 | 2 |
Your task: Calculate the mean daily wage and interpret what it means for the workers.
Experience and Reflections
2 minutes💭 Quick Reflection Questions:
- "What was the most challenging part of finding the mean of grouped data?"
- "How is this different from finding the mean of individual data points?"
- "Can you think of real-life situations where you might need to find the mean of grouped data?"
👥 Student Sharing:
- 2-3 students share their answers to Problem 1
- Teacher provides immediate feedback
- Address any common mistakes observed
- Celebrate successful problem-solving strategies
Assessment Criteria
Students demonstrate mastery by successfully:
Homework & Extension
📚 Assignment:
Research Project: Find one real-life example of grouped data from newspapers, websites, or conduct your own survey. Calculate its mean using the direct method and write a brief interpretation.
💡 Example Sources:
- Economic Data: Income distribution in your city/state
- Demographics: Age groups in your neighborhood
- Consumer Research: Product price ranges in local markets
- Education: Test score distributions from different schools
- Health: Height/weight distributions from health surveys
- Sports: Performance statistics from recent tournaments
Submission Format: Include the original data source, your calculation table, the mean value, and a 2-3 sentence explanation of what the result means.
Materials Needed
Learning Success Indicators
By the end of this 45-minute lesson, students should confidently demonstrate:
Differentiation Strategies
🚀 Advanced Learners
- Introduce problems with unequal class intervals
- Compare direct method vs. assumed mean method
- Analyze multiple datasets simultaneously
- Create their own grouped data problems
🤝 Struggling Learners
- Extra practice with class mark calculations
- Use smaller, simpler numbers initially
- Pair with stronger math partners
- Provide calculation templates
🌍 English Language Learners
- Vocabulary cards with math terms
- Visual aids and real-world examples
- Allow native language for initial understanding
- Peer translation support