Practice Maths

Issues in Data Collection — Solutions

  1. Primary or Secondary Data

    1. Surveying classmates: Primary — you collected it yourself ▶ View Solution
    2. ABS statistics: Secondary — collected by another organisation ▶ View Solution
    3. Recording temperature: Primary — you measured it yourself ▶ View Solution
    4. Newspaper article: Secondary — reported by someone else ▶ View Solution
    5. Weighing school bags: Primary — you measured it yourself ▶ View Solution

  2. Biased or Unbiased?

    1. Every 5th student from roll: Unbiased — systematic random selection from the whole population ▶ View Solution
    2. TV viewers text in vote: Biased — voluntary response; only strong fans bother to vote ▶ View Solution
    3. Student surveys friends: Biased — convenience bias; friends likely share similar views ▶ View Solution
    4. Random patient files: Unbiased — random selection from complete database ▶ View Solution
    5. Online poll, multiple votes: Biased — allows repeat voting; results can be manipulated ▶ View Solution

  3. Identify the Type of Bias

    1. “Wouldn’t you agree…”: Leading question bias — phrasing suggests “yes” is the correct answer ▶ View Solution
    2. 3 people at library: Small sample bias — 3 people cannot represent the whole school ▶ View Solution
    3. Website vote, 12% click: Voluntary response bias — only people with a strong opinion click ▶ View Solution
    4. One Sydney CBD café: Convenience bias — CBD café customers are not representative of all Australians ▶ View Solution
    5. Frustrated commuters call in: Voluntary response bias — only the most frustrated people bother to call ▶ View Solution

  4. Rewrite the Biased Question

    1. “Too much homework is unfair”: Neutral: “How do you feel about the amount of homework you receive?” Options: Too much / About right / Too little ▶ View Solution
    2. “New park design is much better”: Neutral: “How would you rate the new park design compared to the old one?” Options: Much better / Better / About the same / Worse / Much worse ▶ View Solution
    3. “Waste time on your phone”: Neutral: “How many hours per day do you use your phone?” — removes the loaded word “waste” ▶ View Solution
    4. “Unnecessary and costly traffic lights”: Neutral: “What is your opinion of the new traffic lights on Main Street?” Options: Strongly support / Support / Neutral / Oppose / Strongly oppose ▶ View Solution

  5. Problem Solving

    1. Fair survey design: Question: “Which sport do you most enjoy playing at lunch?” (list options); randomly select students from each year group; systematic random sample from the school roll ▶ View Solution
    2. Bus stop convenience sample: Convenience bias — students at the bus stop early likely prefer early/unchanged start; students who prefer a later start are entirely excluded ▶ View Solution
    3. Two problems with newspaper survey: 1. Small sample (15 parents) — too few for a reliable result. 2. Convenience bias — fete attendees are self-selected, more engaged than non-attendees ▶ View Solution

  6. True or False?

    1. Sample always less reliable than census: False — a well-designed random sample can be very reliable; a census can have its own errors ▶ View Solution
    2. Survey of 500 must be accurate: False — size alone doesn’t guarantee accuracy; a biased sample of 500 produces biased results ▶ View Solution
    3. Random selection reduces bias: True — everyone has equal selection chance, reducing systematic bias ▶ View Solution
    4. Biased 1 000 better than unbiased 50: False — bias is scaled up; 1 000 biased responses give a more confidently wrong answer ▶ View Solution

  7. Identify Population and Sample

    1. Queensland teenagers & social media: Population: all Queensland teenagers (Year 7–12)  |  Sample: 400 students across 10 schools ▶ View Solution
    2. Council & dog park: Population: all local residents  |  Sample: 80 people at the community meeting ▶ View Solution
    3. Australian river water quality: Population: all rivers in Australia  |  Sample: 25 rivers ▶ View Solution
    4. Company & Australian households: Population: all Australian households  |  Sample: 1 200 households reached by phone ▶ View Solution

  8. Evaluate and Improve the Method

    1. Only asks top maths class: Problem: convenience bias — top students more likely to enjoy maths. Improvement: randomly select from all Year 7 maths classes ▶ View Solution
    2. Fitness app sleep survey: Problem: self-selection bias — fitness app users are health-conscious with likely better sleep than average. Improvement: random telephone or door-to-door survey from a full population list ▶ View Solution
    3. Monday lunchtime, 60 respond: Problem: convenience bias (only students present that day) and low response rate (60/300). Improvement: randomly select from the school roll across varied contexts ▶ View Solution
    4. Council newsletter, 45 respond: Problem: voluntary response bias — only 45/8 000 responded, skewed towards those with strong opinions. Improvement: random phone survey or door-knock a random sample ▶ View Solution

  9. Data Collection Design

    1. Two sampling methods: Systematic random: survey every 3rd student from the Year 7 roll — easy to implement, ensures spread. Stratified: survey equal numbers from each Year 7 class — ensures all classes represented ▶ View Solution
    2. Why sampling instead of census: Census is sometimes too expensive, time-consuming or impossible. E.g. TV ratings use a sample of households; blood tests use a sample of blood, not all of it ▶ View Solution
    3. Random vs representative; can random be non-representative?: Yes — random gives equal selection chance; representative reflects population proportions. A random sample can by chance overrepresent one group (e.g. 9 of 10 from Year 7) ▶ View Solution

  10. Extended Investigation

    1. Homework investigation:
      1. Problems with Layla’s method: 1. Convenience bias — only her own class surveyed. 2. Timing bias — asking on Friday may distort recall of the week’s workload ▶ View Solution
      2. How these problems affect results: Her class may have an unusually heavy or light load; a single Friday memory may not reflect a typical week ▶ View Solution
      3. Improved method: Randomly select 40–50 students from all Year 7 classes; use an anonymous questionnaire; ask students to record actual time over a full week (not recalled); repeat across multiple weeks ▶ View Solution
    2. News article bias:
      1. Types of bias in the article: Voluntary response bias (chose to respond to a social media post) and self-selection bias (followers of the opposition are already critics of the government) ▶ View Solution
      2. Why larger biased sample isn’t better: Bias is scaled up — 1 200 pre-selected critics produce a more confidently wrong result, not a more accurate one ▶ View Solution
      3. How to conduct the survey fairly: Commission an independent organisation to randomly survey 1 000 Australians from the electoral roll using a neutral question with a balanced rating scale ▶ View Solution