Practice Maths

Topic Review — Statistics

Mixed Practice — L56 – L57

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

Review Questions

  1. Calculating all four measures from large datasets Fluency

    1. The ages of players in a cricket squad are:
      {24, 31, 19, 28, 23, 35, 22, 29, 26, 21, 33, 27, 20, 30, 25}
      Calculate the mean, median, mode, and range.
    2. The number of minutes students spent on homework one evening:
      {45, 60, 30, 75, 45, 90, 55, 45, 70, 50, 65, 40, 80, 45, 55}
      Calculate the mean, median, mode, and range.

  2. Using technology features correctly Fluency

    1. Write the spreadsheet formula you would use to find the range of data in cells B2 to B20.
    2. A student enters a dataset and gets a mean of 0.48, but all the values in the dataset are between 40 and 60. What has most likely gone wrong?
    3. True or false: "If =MODE() returns an error, it means the data was entered incorrectly." Explain your answer.
    4. A dataset has values {12, 14, 13, 15, 12, 14, 16, 13}. Before using technology, estimate the mean. Then confirm by calculating it exactly.

  3. The full inquiry process Understanding

    A student is investigating: "How far do Year 7 students travel to school?"
    She surveys 20 students and records their travel distances (in km):
    {1.2, 3.5, 0.8, 5.1, 2.4, 1.8, 4.2, 0.5, 3.1, 2.7, 1.5, 6.3, 2.0, 3.8, 1.1, 4.5, 2.9, 0.7, 3.3, 2.2}

    1. Calculate the mean, median, and range (round mean to 1 d.p.).
    2. Choose an appropriate display for this data and explain why.
    3. Write two conclusions that directly answer the inquiry question.
    4. Identify one limitation of this study.

  4. Interpreting and communicating results Understanding

    1. Two swimming squads recorded their 50 m freestyle times (seconds):
      Squad A: {32.1, 29.8, 31.4, 30.7, 33.2, 28.9, 31.9, 30.5}
      Squad B: {28.3, 35.6, 27.9, 36.1, 29.4, 34.8, 28.7, 35.2}
      1. Calculate the mean and range for each squad.
      2. Which squad is faster on average? Which is more consistent?
    2. A graph shows that 90% of students passed an exam. The article says this "proves the exam was too easy." Explain why this conclusion may not be valid and what additional information you would need.

  5. Extended problem solving Problem Solving

    1. The daily maximum temperatures (°C) recorded in a town over 14 days were:
      {22, 25, 19, 28, 31, 24, 27, 23, 30, 26, 18, 29, 25, 21}
      1. Calculate mean, median, mode, and range.
      2. Display this data using a stem-and-leaf plot.
      3. Write three conclusions about the weather during this period.
    2. Design a complete statistical inquiry for the question: "Do students who participate in school sport perform better academically?"
      1. Write your precise statistical question.
      2. Describe your data collection plan.
      3. Name a possible confounding factor and explain how it could affect your conclusions.
      4. Explain why this study could show correlation but not prove causation.

  6. Choose the correct formula: Fluency

    1. Write the formula to calculate the mean of a dataset.
    2. How do you find the median when there is an even number of values?
    3. What does the range measure in a dataset?
    4. If a dataset has two values that both appear most often, what is the mode?

  7. Spreadsheet skills: Understanding

    A spreadsheet has data in cells A1:A12.

    1. Write the formula to find the mean.
    2. Write the formula to find the median.
    3. Write the formula to find the minimum value.
    4. Write a formula to find the range (maximum minus minimum).

  8. Critically evaluate a statistic: Understanding

    A news report says: “The average Australian household income is $120,000.”

    1. What measure of centre is likely being used: mean or median? Why?
    2. Why might the mean be misleading for household income?
    3. Which measure would give a better picture of a “typical” household income? Why?

  9. Statistical question or not? Fluency

    Identify each as a statistical question (S) or not statistical (N), and explain:

    1. How tall is the Eiffel Tower?
    2. How many hours per week do Year 7 students spend on screens?
    3. What is the most common blood type in Australia?
    4. How old is Ms Dudley?

  10. Full investigation: A student wants to know which sport is most popular among Year 7 students. Problem Solving

    1. Write a clear statistical question they could investigate.
    2. How would they collect the data? Describe a fair method.
    3. What type of graph would best display the results? Justify your answer.
    4. The results show: football 12, soccer 10, basketball 8, swimming 5, other 5. Write a two-sentence conclusion.
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