Practice Maths

Topic Review — Bivariate Data

Mixed Practice — L40 – L42

This review covers scatter plots and correlation, lines of best fit, and interpreting bivariate data. Try each question before checking your answers.

Review Questions

  1. Scatter plots and correlation fluency. Fluency

    1. Describe the correlation you would expect between a student’s height and the length of their shadow at noon. Give the direction and estimated strength.
    2. For a scatter plot showing daily temperature (x) and hot chocolate sales (y), identify the independent and dependent variables.
    3. A scatter plot has points tightly clustered along a line going from top-left to bottom-right. Describe the correlation.
    4. Give an example of two variables that would show no correlation.
    5. What is an outlier on a scatter plot? How might it affect your description of the correlation?
    6. A scatter plot shows that taller people tend to earn more. Name a likely confounding variable.

  2. Line of best fit fluency. Fluency

    1. A line of best fit has equation y = 4x − 3. Predict y when x = 7.
    2. A line of best fit has equation y = −2.5x + 60. Predict y when x = 16.
    3. The data range for a study is x = 5 to x = 25. A student predicts using x = 30. Is this interpolation or extrapolation?
    4. A line passes through (0, 12) and (6, 42). Find its gradient and write the equation in the form y = mx + c.
    5. True or false: A steeper gradient on a line of best fit means there is a stronger correlation. Explain.
    6. A line of best fit has a negative gradient. What does this tell you about the variables?

  3. Using the line of best fit. Understanding

    1. The line of best fit for hours of revision (x) versus exam score (y, out of 100) is y = 3.2x + 28. Revision data was collected from students who studied 1 to 15 hours.
      1. Predict the score for a student who revised for 10 hours.
      2. A student revised for 25 hours. Is predicting their score using this equation reliable? Why or why not?
      3. What does the gradient of 3.2 mean in context?
      4. What does the y-intercept of 28 represent?

  4. Interpretation and limitations. Understanding

    1. A study of 12 people finds a strong positive correlation between hand size and vocabulary. Identify two problems with drawing a broad conclusion from this finding.
    2. A scatter plot shows ice cream sales and sunburn cases are positively correlated. Explain why this does not mean ice cream causes sunburn. Name the confounding variable.
    3. A researcher wants to study whether caffeine intake affects concentration in Year 9 students. Describe one source of bias in the data collection method: “Students volunteer to fill in an online survey about their daily caffeine intake and self-rate their concentration out of 10.”
    4. A graph of housing prices over 6 months shows a line of best fit y = 12 000x + 450 000. The analyst predicts prices will reach $1 000 000 in the future. Identify the type of prediction and one reason it may be unreliable.

  5. Extended problem solving. Problem Solving

    1. A sports scientist measures the number of training sessions per week (x) and the 100 m sprint time (y, seconds) for 35 junior athletes. The data shows a moderate negative correlation. The line of best fit is y = −0.4x + 14.2. Data was collected from athletes doing 2 to 10 sessions per week.
      1. Predict the sprint time for an athlete doing 7 sessions per week.
      2. Predict for 15 sessions per week. Comment on reliability.
      3. What does the gradient −0.4 mean in this context?
      4. Write a brief statistical conclusion for this study, including one limitation.
    2. Two researchers both study the relationship between screen time and sleep duration in teenagers. Researcher A uses a sample of 400 students from 10 different Queensland schools. Researcher B uses a sample of 12 students from a single school.
      1. Whose results are likely to be more reliable? Give two reasons.
      2. Both researchers find a negative correlation. Researcher A reports moderate strength; Researcher B reports strong strength. Explain why their findings might differ even though the true relationship is the same.
    3. A student says: “I drew a line of best fit on my scatter plot that passes through 8 out of 10 data points. That must be a really good line of best fit!” Explain why this reasoning is flawed and describe what makes a line of best fit good.
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