Practice Maths

Topic Review — Further Data — Solutions

  1. Data Collection Issues

    1. 5 people survey: Small sample bias — 5 people cannot represent all Australian households; random variation has an enormous effect on the result ▶ View Solution
    2. Primary or secondary:
      1. ABS report: Secondary — collected by the ABS, not by you ▶ View Solution
      2. Measure foot lengths: Primary — you measured it yourself ▶ View Solution
      3. Wikipedia population data: Secondary — compiled and published by others ▶ View Solution
    3. Lunchtime sport sample: Biased — convenience bias. Students who attend lunchtime sport already prefer sport at lunchtime; students who prefer other lunch activities are excluded entirely. ▶ View Solution
  2. Evaluating Sources and Biased Questions

    1. Source credibility:
      1. Government road fatalities report: Rating 3 — official government body with transparent methodology and accountability ▶ View Solution
      2. Anonymous blog post: Rating 1 — no source cited, no accountability, anyone can publish anything ▶ View Solution
      3. Peer-reviewed medical journal: Rating 3 — reviewed by experts before publishing; high accountability ▶ View Solution
    2. Rewrite biased question: Neutral version: "How do you feel about the length of the lunch break?" Options: Too short / About right / Too long ▶ View Solution
    3. Type of bias: Voluntary response bias — only followers of the party see and respond; they already support the party, so overwhelmingly positive results are expected ▶ View Solution
  3. Reading the Clearwater Temperature Table

    1. Hottest month: January — 31°C ▶ View Solution
    2. Coldest month: July — 12°C ▶ View Solution
    3. Difference: 31 − 12 = 19°C ▶ View Solution
    4. Months above 20°C: 6 months — Jan (31), Feb (30), Mar (27), Apr (23), Nov (26), Dec (29) ▶ View Solution
    5. Hemisphere: Southern Hemisphere — January is the hottest month (summer in December–February) and July is the coldest (winter). In the Northern Hemisphere, July is hottest and January is coldest. ▶ View Solution
    6. Does it prove no snow?: No — this data shows monthly averages. Even if the average is above freezing, individual days could be colder and produce snow. Also, this may be one year's data and doesn't capture extremes. ▶ View Solution
  4. Full Data Analysis — Quiz Scores

    1. Measures: Sorted: 9,11,12,13,14,14,14,15,15,16,17,17,18,19,20 | Mean=(9+11+12+13+14+14+14+15+15+16+17+17+18+19+20)÷15=224÷15=14.9 | Median=15 (8th value) | Mode=14 | Range=20−9=11 ▶ View Solution
    2. Display type: Stem-and-leaf plot — shows individual values and overall distribution shape for this moderate-sized dataset. Stems: 0|9, 1|1 2 3 4 4 4 5 5 6 7 7 8 9, 2|0 ▶ View Solution
    3. Mean ≈ median means symmetric?: Not necessarily valid. While a symmetric distribution often has mean ≈ median, it is possible for a skewed dataset to coincidentally have similar mean and median. You need to look at the actual display to judge symmetry. ▶ View Solution
  5. Writing Conclusions and Evaluating Claims

    1. 100 m run comparison:
      1. Mean and range: Group 1: Mean=(13.2+12.8+14.1+13.5+12.9+13.7+14.3+13.0)÷8=107.5÷8=13.4 s, Range=14.3−12.8=1.5 s | Group 2: Mean=(15.4+18.2+16.7+14.9+17.3+19.1+15.8+16.2)÷8=133.6÷8=16.7 s, Range=19.1−14.9=4.2 s ▶ View Solution
      2. Comparison paragraph: Sample: "The trained athletes (Group 1) ran 100 m significantly faster on average, with a mean time of 13.4 s compared to 16.7 s for the general students. Group 1 was also far more consistent, with a range of only 1.5 s versus 4.2 s. This suggests that athletic training not only improves average speed but also reduces variability in performance." ▶ View Solution
    2. Reading and vocabulary claim:
      1. Strength and weakness: Strength: actual measured data from 50 students provides numerical support. Weakness: 50 students from (presumably) one school is a small, potentially unrepresentative sample. ▶ View Solution
      2. Why headline might be misleading: The headline uses the word "scores higher" which implies causation, but the study only shows correlation. It also doesn't mention the sample size (50) or that it may be limited to one school, giving the impression of a large, definitive study. ▶ View Solution
      3. Confounding factor: Sample: parental education level. Parents with higher education may encourage both more reading AND better vocabulary development through conversation at home. The reading itself may not be the direct cause. ▶ View Solution