Census vs Sample Practice

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📊 Part 1: Census or Sample?

1. A school principal wants to find out what students think about the new uniform policy. The school has 1,200 students. Should they use a census or sample?

Census - survey all 1,200 students

Sample - survey a representative group

Sample - surveying a representative group would save time and resources while still providing useful insights.

2. The Australian Bureau of Statistics wants to count how many people live in Australia. Should they use a census or sample?

Census - count everyone

Sample - count a representative group

Census - it is essential to count everyone to get an accurate population figure.

3. A chocolate company wants to test if their new recipe tastes good. They have 50,000 chocolate bars ready to sell. Should they use a census or sample?

Census - test all 50,000 bars

Sample - test a small number of bars

Sample - testing a small number of bars can provide a good indication of overall quality without the need to test every single bar.

4. Which of these are advantages of using a sample instead of a census? (Choose all that apply)

Faster to collect data

Less expensive

Gives you data about every individual

Requires fewer people to help

Faster to collect data, Less expensive, Requires fewer people to help.

⚠️ Part 2: Identifying Bias

5. A researcher wants to find out how much time teenagers spend on social media. They decide to survey students outside a gaming arcade at 2pm on a Tuesday. What is wrong with this sampling method?

This method is biased because it only targets teenagers who are at the arcade, excluding those who may not visit gaming locations.

6. A council wants to know if residents support building a new skate park. They survey people by calling home phone numbers between 9am-3pm on weekdays. Identify the bias in this sampling method.

The bias arises because many residents may be at work during these hours, leading to an unrepresentative sample of the community.

7. Which sampling method would give the most reliable results for finding out students' favourite school subject?

Survey students in the library during lunch

Survey every 10th student on the class roll from all year levels

Survey students in the maths classroom

Survey students who volunteer to participate

Survey every 10th student on the class roll from all year levels - this method ensures a more diverse and representative sample.

✏️ Part 3: Justify Your Choice

8. A local cinema wants to decide what movies to show next month. They have a database of 5,000 regular customers. Should they use a census or sample? Explain your reasoning, including at least two factors that influenced your decision.

Sample - it would be impractical to survey all 5,000 customers. A sample can provide insights while saving time and resources. Factors include the cost of surveying all customers and the time required to analyze the data.

9. Design a sampling method to find out how many hours per week Year 9 students in Australia spend doing homework. Describe your method and explain how you would avoid bias.

I would randomly select Year 9 students from various schools across Australia to ensure diversity. To avoid bias, I would ensure that the sample includes students from different backgrounds and locations.

10. A restaurant owner notices that customer complaints have increased. The restaurant serves 200 customers per day. Would you recommend a census or sample to investigate customer satisfaction? Give three reasons for your choice.

Sample - it is more efficient to survey a smaller group of customers. Reasons: 1) It saves time and resources, 2) It allows for quicker analysis of results, 3) It can still provide a representative view of customer satisfaction.