📊 Part 1: Understanding Population and Variation
1. A researcher wants to study the average height of Year 11 students in New Zealand. Which of the following best describes the population?
All students at one Auckland school
All Year 11 students in New Zealand
100 randomly selected Year 11 students
All students in New Zealand
2. Which factors could contribute to variation in student test scores? (Select all that apply)
Study time
Prior knowledge
Test anxiety
Random chance
Teaching quality
3. The weights of kiwi birds in a sanctuary range from 1.2kg to 3.8kg. The variation in weight is most likely due to:
Measurement error only
Natural biological differences
All birds being identical
Poor data collection
4. A sample of 50 students from a population of 2000 shows test scores ranging from 45% to 95%. This demonstrates:
No variation exists
High variation in the sample
Low variation in the sample
Invalid data collection
✏️ Part 2: Applied Understanding
5. A café owner wants to determine the average amount customers spend. Define the population and suggest what might cause variation in spending amounts.
6. Complete the following statement: "In statistics, a _____________ is the entire group we want to study, while _____________ refers to the differences we observe between individual data points."
7. A researcher measures the daily temperature in Auckland for 30 days and finds temperatures ranging from 8°C to 22°C. Explain two different sources that could contribute to this variation.
8. Extension Challenge: A school has 800 students. Describe how you would select a representative sample of 80 students to study average study hours per week. What factors might cause variation in your results?
🎯 Success Criteria & Reflection
9. Self-Assessment: Check off what you can now confidently do:
Define what a population is in statistics
Identify sources of variation in data
Distinguish between natural variation and measurement error
Explain why variation is important in statistical analysis
10. Reflection: Write one real-world example where understanding population variation would be important for decision-making.
Teacher Notes:
Differentiation: Questions 1-4 focus on recognition, 5-7 on application, 8 provides extension. Students struggling with concepts should focus on questions 1-6. Advanced students should complete all questions and create their own population study scenario.
