Practice Maths

Secondary Source Data — Solutions

  1. City Population Table

    1. Largest population: Sydney — 5 231 thousand ▶ View Solution
    2. Smallest population: Adelaide — 1 402 thousand ▶ View Solution
    3. Sydney + Melbourne: 10 309 thousand ▶ View Solution
    4. Brisbane − Perth: 368 thousand ▶ View Solution
    5. Total all five cities: 16 463 thousand ▶ View Solution
  2. Subject Average Scores Table

    1. Highest average: Art — average score 84 ▶ View Solution
    2. Lowest average: History — average score 61 ▶ View Solution
    3. Highest − Lowest: 23 marks ▶ View Solution
    4. Subjects above 70: 4 subjects — Maths (72), Science (75), Art (84), PE (79) ▶ View Solution
    5. Average of all averages: 73.2 ▶ View Solution
  3. Evaluate Source Credibility

    1. ABS 2024 dataset: Rating 3 — government statistical authority, up to date, transparent methods ▶ View Solution
    2. Social media comment: Rating 1 — no source cited, no evidence of research, anyone can post anything ▶ View Solution
    3. Peer-reviewed journal article: Rating 3 — reviewed by other experts before publishing; researchers have accountability ▶ View Solution
    4. Company’s own website: Rating 1 — financial interest in claims; no independent verification ▶ View Solution
    5. Government health report 2019: Rating 2 — generally credible but may not be current; check for newer data ▶ View Solution
  4. Does the Data Support the Claim?

    1. Art highest score: Supports — Art (84) is the highest value in the table ▶ View Solution
    2. Year 7 across Australia: Goes beyond the data — the table covers only one school; cannot generalise to all of Australia ▶ View Solution
    3. Maths higher than History: Supports — Maths (72) > History (61) ▶ View Solution
    4. Students dislike History because boring: Does not support — data shows scores, not attitudes; low scores don’t tell us why ▶ View Solution
    5. More than half above 70: Supports — 4 of 6 subjects have averages above 70 ▶ View Solution
  5. Statistical Inquiry with Secondary Data

    1. Statistical question: “How has the median household income in Australia changed over the past 20 years?” ▶ View Solution
    2. ABS dataset: ABS Survey of Income and Housing — records household income across Australia; conducted regularly so trend data is available ▶ View Solution
    3. Two limitations: 1. Data may not match the exact year or population being studied. 2. ABS definition of “household” may differ from the measure required ▶ View Solution
    4. Confounding factor: Inflation — if income grew 10% but prices grew 15%, people are worse off; comparing dollar amounts without adjusting for inflation is misleading ▶ View Solution
  6. Riverside Rainfall Table

    1. Highest rainfall month: February — 102 mm ▶ View Solution
    2. Lowest rainfall month: July — 19 mm ▶ View Solution
    3. Total annual rainfall: 696 mm ▶ View Solution
    4. Average monthly rainfall: 58.0 mm ▶ View Solution
    5. Months with more than 60 mm: 5 months — Jan, Feb, Mar, Oct, Dec ▶ View Solution
    6. Difference wettest vs driest: 83 mm ▶ View Solution
    7. Which half had greater rainfall: Jan–Jun (390 mm) vs Jul–Dec (306 mm) — Jan–Jun had greater rainfall ▶ View Solution
    8. Seasonal trend: Wet summer/autumn (Jan–Mar); dry winter (Jun–Aug); rainfall increases again through spring into summer ▶ View Solution
  7. Correlation or Causation?

    1. Breakfast and test scores: Correlation (possibly causation) — relationship exists but other factors (sleep, home environment) may be involved ▶ View Solution
    2. Ice cream and shark attacks: Spurious correlation — both caused by hot weather; ice cream does not cause shark attacks ▶ View Solution
    3. Libraries and literacy: Correlation — cities may have higher education investment overall; libraries not the sole cause ▶ View Solution
    4. Light switch and light: Causation — switch directly completes the electrical circuit ▶ View Solution
    5. Chocolate and Nobel Prizes: Spurious correlation — wealthier countries tend to have both; chocolate doesn’t cause genius ▶ View Solution
    6. Exercise and heart disease: Likely causation — supported by medical research; diet and other habits also play a role ▶ View Solution
  8. Limitations of Secondary Data

    1. 2010 census for today: Data is 15+ years old; population and living conditions have changed significantly ▶ View Solution
    2. Mining industry wage data: Mining workers not representative; industry pays above-average wages, overestimating typical wages ▶ View Solution
    3. US study for Australian teenagers: Cultural, social, and economic differences mean results may not transfer to Australia ▶ View Solution
    4. City weather stations for rural Australia: Urban heat island effect; city data may not reflect rural or remote conditions ▶ View Solution
    5. Limitation vs bias: Limitation restricts scope of conclusions; bias is a systematic error that makes conclusions inaccurate ▶ View Solution
  9. Screen Time Table

    1. Highest screen time: 16–18 age group — 41 hours per week ▶ View Solution
    2. Lowest screen time: 6–9 age group — 14 hours per week ▶ View Solution
    3. Increase from 6–9 to 13–15: 21 hours per week ▶ View Solution
    4. Average across all groups: 30 hours per week ▶ View Solution
    5. Does it always increase with age?: No — drops from 41 to 38 for the 19–25 age group; claim is not fully supported ▶ View Solution
    6. One limitation: Single study in one location; sample size and methodology not given ▶ View Solution
  10. Extended Analysis — Height and Shoe Size

    1. Trend: As height increases, shoe size increases — from 5.2 (140–149 cm) to 9.1 (170–179 cm) ▶ View Solution
    2. Correlation, causation, or both?: Correlation; likely causal (overall body growth drives both) but this table alone doesn’t prove causation ▶ View Solution
    3. Two limitations: 1. Small sample (50 students). 2. Grouped data hides individual variation within each height range ▶ View Solution
    4. Evaluate the conclusion: “Proves” overstates it; better: “suggests a positive relationship consistent with overall growth patterns” ▶ View Solution
    5. Additional information needed: Whether both genders were included; whether students were randomly selected from multiple schools ▶ View Solution