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📖 Lesson 14 ⏱ ~30 min Year 10 · Unit 4 ⚡ +50 XP

Bivariate Data Review

Consolidate skills in analysing bivariate data through scatter plots, correlation and lines of best fit.

Today's hook:
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Core learning
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Worksheet

Worksheet

Use the worksheet to complete this lesson in your book or digitally.

Warm-up
Think First
+5 XP each

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.

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Intentions

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.
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Key Terms

Key Terms

Bivariate analysis — Statistical methods for exploring relationships between two variables.
Trend — The general direction or pattern shown by data points.
Prediction — Using a model to estimate an unknown value based on known data.
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Misconceptions

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.

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From the lesson
Content

Bivariate Data Review

Work through the content, activities and worked examples below. Test your understanding with the questions in the Questions phase.

Remember Probability = (number of favourable outcomes) / (total number of possible outcomes). Always check that your answer is between 0 and 1.
Exam Tip When answering probability questions, show your working as a fraction first, then convert to a decimal or percentage if required.
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From the lesson
Activity
✏ Activity 1 — Basic Probability

Calculate the probability of each event:

  1. Rolling a 6 on a fair die.
  2. Drawing a red card from a standard deck.
  3. Flipping two heads in a row.
  4. Drawing a heart or a diamond from a standard deck.
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From the lesson
Worked Example

Worked Example

Step-by-step
A bag contains 5 red, 3 blue and 2 green marbles. One marble is drawn at random. Find the probability of drawing: (a) a red marble, (b) a blue or green marble, (c) not a red marble.
  1. 1
    Step 1: Total marbles = 5 + 3 + 2 = 10.
  2. 2
    (a) P(red): 5 red out of 10 total. P(red) = 5/10 = 1/2 = 0.5.
  3. 3
    (b) P(blue or green): 3 blue + 2 green = 5 favourable. P(blue or green) = 5/10 = 1/2 = 0.5.
  4. 4
    (c) P(not red): Using the complement rule, P(not red) = 1 − P(red) = 1 − 0.5 = 0.5.
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From the lesson
Revisit

Revisit Your Thinking

Look back at your Think First response. What new understanding do you have now?

Reflect
Revisit your thinking
reflect

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?

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Multiple Choice

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:

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From the lesson
Short Answer

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.

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