Practice Maths

Topic Review — Data Collection and Statistics — Solutions

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  1. Data collection methods

    1. Primary or secondary:
      1. Student surveys classmates:
      2. BOM rainfall records:
      3. Teacher records class scores:
      4. ABS unemployment figures:
    2. Population and sample:
      1. Factory bottles:
      2. Council survey:
    3. Sampling methods:
      1. Every 8th customer:
      2. Names from a hat:
      3. 20 from each year level:
      4. First 10 friends:

  2. Evaluating data displays

    1. Bias and misleading features:
      1. Y-axis starting at 950:
      2. Pie chart adding to 105%:
      3. Leading survey question:
    2. Best measure of centre for right-skewed data:
    3. Misleading pictograph:

  3. Measures of centre and spread

    1. Mean:
    2. Median:
    3. Mode:
    4. Range:
    5. Equal means — do the groups exercise similarly?:
    6. Which measure better reveals the difference?:

  4. Effect of sample size

    1. Coin flipping:
      1. Theoretical probability of heads:
      2. Trend in relative frequency:
      3. Is coin unfair after 10 flips?:
    2. Marble draws:
      1. Relative frequency approaching:
      2. Estimated proportion of red:
      3. Estimated number of red marbles (30 total):

  5. Extended data investigation

    1. Canteen survey problems:
      1. Two problems:
      2. Better method:
      3. Students per year level:
    2. School heights:
      1. Mean and range:
      2. More consistent school:
      3. Limitation: