Interpreting Statistical Information

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Part 1: Identify the Statistical Information

Instructions: Read each situation carefully. Identify the purpose, population, sample, variables, data source and context. Explain your thinking using complete sentences where requested.

1. A Christchurch school surveys 80 Year 12 students about how they travel to school. The school wants to plan safer cycle storage and pedestrian routes.

a) What is the purpose of collecting the information?

b) Identify the population and the sample.

2. In the survey above, name one categorical variable and one numerical variable that could be collected.

3. Which data source is being used in the school survey?

A government census

A school survey

A weather station

A newspaper article

4. A social media post says, “Most New Zealand teenagers exercise every day.” It is based on responses from 25 teenagers who chose to complete an online poll. Explain one reason why this conclusion may not represent all New Zealand teenagers.

Part 2: Read and Interpret Statistical Displays

Instructions: Use the information in each display. Focus on what the data means in context, not only on finding numbers.

5. Bar graph data: A survey of 120 Auckland students recorded their preferred summer activity.

Swimming: 42 Walking: 30 Team sport: 24 Cycling: 18 Other: 6

a) Which activity was most popular?

b) Write one statement that compares swimming with cycling.

6. Histogram data: The table below describes the weekly screen time of 50 Year 12 students. Each interval includes the lower value but not the upper value.

Hours per week: 0–<5: 4 students 5–<10: 11 students 10–<15: 17 students 15–<20: 12 students 20–<25: 6 students

a) Which interval contains the greatest number of students?

b) Is it reasonable to say that most students spend at least 15 hours per week on screens? Explain.

7. Time-series graph data: The number of passengers using a Wellington train station was recorded each month.

January: 18,000 February: 17,500 March: 19,000 April: 20,500 May: 21,000 June: 20,000

Describe the overall trend and identify the month with the highest number of passengers.

8. Pie chart data: A community group asked 200 households how they usually dispose of food scraps: composting 40%, council collection 25%, rubbish bin 30%, and other methods 5%.

a) How many households used council collection?

b) Write one conclusion that could help the community group plan its services.