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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: Did the new training plan actually work? How do you compare 'before' and 'after' fairly?
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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 analysisExamining two or more data sets to identify similarities and differences.
Centre comparisonComparing means or medians to determine which group has higher typical values.
Spread comparisonComparing ranges or IQRs to determine which group has more variability.
Shape comparisonComparing 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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