Practice Maths

Topic Review — Further Data

Mixed Practice — L53 – L55

This review covers all lessons in the Further Data topic. Try each question before checking your answers.

Review Questions

  1. Data collection issues Fluency

    1. A researcher surveys 5 people to determine the average Australian household income. What type of bias is this, and why is it a problem?
    2. Classify each as primary or secondary data:
      1. You read an ABS report on unemployment rates.
      2. You measure the foot length of every student in your class.
      3. You find population data on Wikipedia.
    3. A student wants to know whether Year 7 students prefer morning or afternoon sport. She asks only students who turn up to lunchtime sport practice. Is this sample biased or unbiased? Explain.

  2. Evaluating sources and identifying bias in questions Fluency

    1. Rate each source from 1–3 for credibility and give a reason:
      1. A government report on road fatalities published by the Bureau of Infrastructure, Transport and Regional Economics.
      2. An anonymous blog post claiming "most teenagers are addicted to their phones."
      3. A peer-reviewed study on sleep deprivation published in a medical journal.
    2. Rewrite this biased question as a neutral one: "Don't you think it's ridiculous that we only get 30 minutes for lunch?"
    3. Identify the type of bias in this scenario: A political party posts a poll on their own social media page asking followers whether they support the party's new policy.

  3. Reading data tables Understanding

    Average monthly temperature (°C) — Clearwater (fictional city)

    Month JanFebMarAprMayJun JulAugSepOctNovDec
    Temp (°C) 313027231814 121317212629
    1. Which month is the hottest?
    2. Which month is the coldest?
    3. What is the difference between the hottest and coldest monthly temperatures?
    4. How many months have an average temperature above 20°C?
    5. In which hemisphere (Northern or Southern) is Clearwater likely to be? Explain using the data.
    6. Does this data prove that it never snows in Clearwater? Explain.

  4. Full data analysis Understanding

    The scores (out of 20) for a class quiz are: {14, 17, 12, 19, 15, 11, 18, 14, 16, 14, 13, 20, 9, 17, 15}

    1. Calculate the mean, median, mode, and range.
    2. Describe the display type you would choose for this data and why.
    3. A student says "The mean and median are almost the same, so the data must be symmetric." Is this a valid conclusion? Explain.

  5. Writing conclusions and evaluating claims Problem Solving

    1. Two groups of students were timed running 100 m (in seconds):
      Group 1 (trained athletes): {13.2, 12.8, 14.1, 13.5, 12.9, 13.7, 14.3, 13.0}
      Group 2 (general students): {15.4, 18.2, 16.7, 14.9, 17.3, 19.1, 15.8, 16.2}
      1. Calculate the mean and range for each group.
      2. Write a paragraph comparing the two groups' times using the measures you calculated.
    2. A newspaper headline states: "Children who read more books score 20 points higher on vocabulary tests." This is based on a survey of 50 primary school students.
      1. Identify one strength and one weakness of this study.
      2. Explain why the headline's claim might be misleading.
      3. Suggest one confounding factor that could explain the correlation between reading and vocabulary scores without reading being the direct cause.

  6. Classify each variable: Fluency

    For each variable, state whether it is categorical or numerical, and if numerical whether it is discrete or continuous:

    1. The colour of cars in a car park
    2. The number of goals scored in a match
    3. The height of students in a class
    4. The type of sport students prefer
    5. The temperature at noon each day
    6. The number of siblings a student has

  7. Sample size and reliability: Understanding

    1. A student surveys 3 classmates to find the most popular music genre at their school. Give two reasons why this sample is unreliable.
    2. What is the difference between a census and a sample?
    3. Give one situation where a census would be better than a sample, and one situation where a sample is more practical.

  8. Evaluate this claim: Understanding

    A social media post states: “9 out of 10 dentists recommend this toothpaste.”

    1. What information would you need to evaluate this claim properly?
    2. Suggest two ways this statistic could be misleading.
    3. Write a more informative version of this statistic.

  9. Correlation or causation? Problem Solving

    1. A study finds that students who eat breakfast score higher on tests. Does this prove that eating breakfast causes better test scores? Explain.
    2. Ice cream sales and drowning rates both increase in summer. Does ice cream cause drowning? What is the real explanation?
    3. What is a confounding variable? Give your own example.

  10. Plan a data investigation: Problem Solving

    You want to investigate: “Do Year 7 students who sleep more than 8 hours perform better in sport?”

    1. Is this question statistical? Why or why not?
    2. Describe how you would collect data. What would you measure?
    3. Identify one potential source of bias in your data collection.
    4. What type of display would you use to show your results?
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