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๐Ÿ“– Lesson 12 โฑ ~30 min Year 10 ยท Unit 4 โšก +50 XP

Scatter Plots and Correlation

Construct scatter plots for bivariate data and describe the correlation as positive, negative or none.

Today's hook:
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Core learning
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From the lesson
Worksheet

Worksheet

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

Warm-up
Think First
+5 XP each

Q1 ยท Do you think taller people tend to have bigger feet? How would you check if there is actually a relationship?

Q2 ยท If you plotted study hours against test scores, what pattern would you expect? Would it always be a perfect straight line?

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From the lesson
Intentions

Learning Intentions

Know

  • Bivariate data involves two variables for each individual. A scatter plot shows the relationship between them.

Understand

  • Why correlation describes the direction and strength of a linear relationship, but does not imply causation.

Can Do

  • Draw scatter plots, identify correlation direction and strength, and explain that correlation โ‰  causation.
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From the lesson
Key Terms

Key Terms

Bivariate data โ€” Data involving two variables measured for each individual or item.
Scatter plot โ€” A graph displaying points for two numerical variables on perpendicular axes.
Positive correlation โ€” As one variable increases, the other tends to increase.
Negative correlation โ€” As one variable increases, the other tends to decrease.
No correlation โ€” No apparent linear relationship between the variables.
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From the lesson
Misconceptions

Misconceptions to Fix

โœ—

Wrong: A strong correlation means the relationship is linear.

โœ“

Right: A correlation coefficient close to ยฑ1 describes the strength of a LINEAR relationship only. Data with a perfect curve can have r = 0 even though there is a clear pattern.

โœ—

Wrong: A correlation of โˆ’0.9 is weaker than +0.5 because it is negative.

โœ“

Right: Correlation STRENGTH is determined by the absolute value. |โˆ’0.9| > |+0.5|, so โˆ’0.9 indicates a stronger relationship than +0.5, just in the opposite direction.

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From the lesson
Content

Scatter Plots and Correlation

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

Remember Line of best fit: roughly equal points above and below, passes through (xฬ„, ศณ), minimises overall distance from points.
HSC Note When drawing a line of best fit by eye, use a ruler and ensure the line passes through the "centre of mass" of the points (xฬ„, ศณ).
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From the lesson
Activity
โœ Activity 1 โ€” Draw a Line of Best Fit

For each scatter plot, draw a line of best fit by eye and estimate the gradient:

  1. Points: (1,2), (2,4), (3,5), (4,7), (5,8)
  2. Points: (1,10), (2,8), (3,7), (4,5), (5,3)
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From the lesson
Worked Example

Worked Example

Step-by-step
Draw a line of best fit for the data: (2, 15), (4, 22), (6, 28), (8, 35), (10, 40). Use it to predict y when x = 7.
  1. 1
    Step 1: Plot the points on a scatter plot with x from 0 to 12 and y from 0 to 50.
  2. 2
    Step 2: Find the centre point: xฬ„ = 6, ศณ = 28. The line should pass through (6, 28).
  3. 3
    Step 3: Draw a line with roughly equal points above and below, passing through (6, 28).
  4. 4
    Step 4: When x = 7, read up to the line and across to y. Estimated y โ‰ˆ 31.
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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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From the lesson
Multiple Choice

Multiple Choice

Select the best answer for each question.

1 mark If points on a scatter plot trend upward from left to right, this shows:

1 mark Height and shoe size typically show:

1 mark The number of ice creams sold and the number of umbrellas sold would likely show:

1 mark Strong correlation between two variables means:

1 mark Which statement is always true?

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From the lesson
Short Answer

Short Answer

Show all working and justify your answers.

1. 4 marks The following data shows the relationship between study time (hours) and test score (%):
(1, 45), (2, 52), (3, 58), (4, 65), (5, 72), (6, 78)
(a) Draw a scatter plot and a line of best fit.
(b) Use your line to predict the test score for 4.5 hours of study.
(c) Is this prediction interpolation or extrapolation? Explain.

2. 3 marks A line of best fit for data ranging from x = 10 to x = 50 is used to predict y when x = 80. Explain why this prediction may be unreliable.

3. 2 marks Explain why the line of best fit should pass through the point (xฬ„, ศณ).

Marking guidance: 1 mark each for MCQs. See mark allocations for each short answer question.

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