Bivariate Data Review
Consolidate skills in analysing bivariate data through scatter plots, correlation and lines of best fit.
Printable Worksheets
Print or save as PDF, or build a custom worksheet from any module's questions.
Worksheet
Use the worksheet to complete this lesson in your book or digitally.
Q1 · What is the difference between data about one thing, like height, and data about two things together, like height and weight?
Q2 · If two variables are correlated, does that mean one causes the other? Give a real-world example where this might not be true.
Learning Intentions
Know
- All techniques for displaying and analysing bivariate data: scatter plots, correlation description, and lines of best fit.
Understand
- How to select and apply the appropriate technique for a given bivariate data set and research question.
Can Do
- Analyse a bivariate data set from start to finish: display, describe correlation, fit a line and make predictions.
Key Terms
Misconceptions to Fix
Wrong: Probability can be greater than 1.
Right: Probability always lies between 0 (impossible) and 1 (certain). It can be expressed as a fraction, decimal or percentage.
Wrong: If P(A) = 0.7, then the probability of A not occurring is 0.3 only if A and B are independent.
Right: P(A′) = 1 − P(A) always. This is the complement rule and does not require independence.
Bivariate Data Review
Work through the content, activities and worked examples below. Test your understanding with the questions in the Questions phase.
Calculate the probability of each event:
- Rolling a 6 on a fair die.
- Drawing a red card from a standard deck.
- Flipping two heads in a row.
- Drawing a heart or a diamond from a standard deck.
Worked Example
Step-by-step-
1Step 1: Total marbles = 5 + 3 + 2 = 10.
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2(a) P(red): 5 red out of 10 total. P(red) = 5/10 = 1/2 = 0.5.
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3(b) P(blue or green): 3 blue + 2 green = 5 favourable. P(blue or green) = 5/10 = 1/2 = 0.5.
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4(c) P(not red): Using the complement rule, P(not red) = 1 − P(red) = 1 − 0.5 = 0.5.
Revisit Your Thinking
Look back at your Think First response. What new understanding do you have now?
Earlier you were asked: What was your first thought on this topic?
Now that you've worked through the lesson, write a fuller answer. What changed in your thinking?
Multiple Choice
Select the best answer for each question.
1 mark The first step in analysing bivariate data is to:
1 mark If a scatter plot shows points scattered randomly with no pattern, there is:
1 mark A line of best fit is most appropriate when the scatter plot shows:
1 mark When interpreting bivariate data, it is important to remember that:
1 mark To compare the relationship between study time and test scores, you would use:
Short Answer
Show all working and justify your answers.
1. 4 marks A spinner has 8 equal sections numbered 1 to 8.
(a) Find the probability of spinning an even number.
(b) Find the probability of spinning a number greater than 5.
(c) Find the probability of spinning a prime number.
2. 3 marks A bag contains 12 marbles: 4 red, 5 blue and 3 green. Two marbles are drawn with replacement. Find the probability that both marbles are blue.
3. 3 marks Explain the difference between theoretical probability and experimental probability. Give an example of each.
Marking guidance: 1 mark each for MCQs. See mark allocations for each short answer question.