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📖 Lesson 11 ⏱ ~30 min Year 10 · Unit 4 ⚡ +50 XP

Comparing Data Sets

Compare two or more data sets using measures of centre, spread, and graphical displays.

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 · If School A has an average HSC score of 85 and School B has 82, does that mean School A is definitely better? What else would you want to know?

Q2 · How could two classes have the same average test score but very different "shapes" of results underneath?

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From the lesson
Intentions

Learning Intentions

Know

  • When comparing data, consider centre (mean/median), spread (range/IQR/SD) and shape (symmetry/skew).

Understand

  • How to write a comparative statement that references centre, spread and shape with numerical evidence.

Can Do

  • Compare distributions using parallel box plots, back-to-back stem-and-leaf plots, and summary statistics.
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From the lesson
Key Terms

Key Terms

Comparative analysis — Examining two or more data sets to identify similarities and differences.
Centre comparison — Comparing means or medians to determine which group has higher typical values.
Spread comparison — Comparing ranges or IQRs to determine which group has more variability.
Shape comparison — Comparing symmetry or skewness between distributions.
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From the lesson
Misconceptions

Misconceptions to Fix

✗

Wrong: The data set with the higher mean is always better.

✓

Right: Whether a higher mean is 'better' depends entirely on context. For test scores, higher is better; for injury rates, lower is better. Always interpret statistics in context.

✗

Wrong: You can fully compare two data sets using only one statistic.

✓

Right: A complete comparison requires BOTH a measure of centre (mean or median) AND a measure of spread (range, IQR, or standard deviation). A single statistic never tells the whole story.

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From the lesson
Content

Comparing Data Sets

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

Remember Positive correlation: as x increases, y tends to increase. Negative correlation: as x increases, y tends to decrease. No correlation: no clear pattern.
Warning Correlation ≠ Causation. Example: Ice cream sales and drowning incidents are positively correlated, but neither causes the other — both are linked to hot weather (a confounding variable).
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From the lesson
Activity
✏ Activity 1 — Identify Correlation

For each pair of variables, state whether you expect positive, negative or no correlation:

  1. Hours studied and test score
  2. Temperature and heating bill
  3. Shoe size and IQ
  4. Age of a car and its value
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From the lesson
Worked Example

Worked Example

Step-by-step
A scatter plot shows the relationship between hours studied and test scores for 10 students. Describe the correlation.
  1. 1
    Step 1: Observe the overall pattern. As hours studied increases, test scores tend to increase.
  2. 2
    Step 2: The points cluster around an imaginary line sloping upwards.
  3. 3
    Step 3: This indicates a positive correlation.
  4. 4
    Step 4: However, this does not mean studying causes higher scores. Other factors (ability, sleep, prior knowledge) also play a role.
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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 When comparing two classes' test scores, the first thing to compare is typically:

1 mark If Class A has IQR = 5 and Class B has IQR = 15, Class B's scores are:

1 mark A good comparative statement should include:

1 mark Parallel box plots make it easy to compare:

1 mark If two data sets have the same median but different IQRs, they have:

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From the lesson
Short Answer

Short Answer

Show all working and justify your answers.

1. 3 marks A study finds a strong positive correlation between the number of firefighters sent to a fire and the amount of damage caused. Does this mean sending more firefighters causes more damage? Explain.

2. 3 marks Sketch a scatter plot showing: (a) strong positive correlation, (b) weak negative correlation, (c) no correlation.

3. 3 marks Give a real-world example where two variables are correlated but one does not cause the other. Identify the confounding variable.

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

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