AQA A-Level Mathematics Paper 3, June 2025: Question 13

1 mark · Easy difficulty · Short Answer

Identify which of the four scatter diagrams corresponds to a product moment correlation coefficient of 0.47.

Practise this question

Question

Question 13 presents four scatter plots with variable A on the horizontal axis and variable B on the vertical axis, asking to identify which diagram shows a product moment correlation coefficient of 0.47. Top-left shows strong positive correlation. Top-right shows strong negative correlation. Bottom-left shows moderate negative correlation. Bottom-right shows moderate positive correlation with wider scatter.

Mark scheme

Show the mark scheme Mark scheme for Question 13 specifies award of B1 mark for ticking the bottom right box, representing moderate positive correlation, under AO 2.2b.

How to answer it

Interpreting the Product Moment Correlation Coefficient (PMCC)

📌 What this question tests

This question assesses your visual understanding of bivariate data and the product moment correlation coefficient ( r ):

  • Recognising the distinction between positive ( r > 0 ) and negative ( r < 0 ) linear relationships.
  • Estimating the strength of linear correlation based on the scatter of points about a line of best fit (weak/moderate vs strong).
  • Matching a numerical coefficient ( r = 0.47 ) to a qualitative scatter pattern.

Question 13

Identifying the Scatter Diagram for r = 0.47  •  [1 Mark]

✅ Correct Answer

Tick the bottom-right box.

Mark Scheme Breakdown:
• [B1] (AO 2.2b) Selecting/ticking the bottom-right diagram.

💡 Key Knowledge

  • Sign of r: Since r = +0.47 is positive, as A increases, B tends to increase (upward trend from left to right).
  • Magnitude of r:
    • |r| ≈ 1 : Points lie very close to a straight line (strong).
    • |r| ≈ 0.4 – 0.5 : Points have noticeable spread around the line, showing a moderate/weak trend.
    • |r| ≈ 0 : No linear pattern (random cloud).

📐 Diagram-by-Diagram Deduction

  1. Step 1: Check the sign (Direction)
    The given value is r = +0.47 (positive). This immediately eliminates diagrams showing a downward trend:
    • Top-right: Shows a very clear downward slope ( r ≈ -0.95 ). Eliminate.
    • Bottom-left: Shows a moderately scattered downward slope ( r ≈ -0.50 ). Eliminate.
  2. Step 2: Assess the strength (Scatter)
    We are left with the top-left and bottom-right diagrams:
    • Top-left: The points form a tight, narrow band tightly clustered along a line. This represents very strong positive correlation ( r ≈ +0.90 to +0.98 ).
    • Bottom-right: The points show a general upward drift, but they are relatively widely dispersed. This represents moderate positive correlation ( r ≈ +0.47 ).
  3. Conclusion: The bottom-right scatter plot is the only one matching both a positive direction and a moderate strength.

🧠 Exam Technique & Strategy

  • Two-Step Rule: Always determine the sign first (rule out 2 options), then determine the closeness to 1 (rule out 1 more).
  • Reference Benchmarks:
    • Values above 0.8 look like tight tubes or nearly straight lines.
    • Values around 0.4 – 0.5 look like broad, loose oval clouds tilted in one direction.
  • Only tick one box as explicitly instructed. If you change your mind, cross out the incorrect tick cleanly.

❌ Common Misconceptions

  • Confusing the top-left plot: Students frequently equate any positive pattern with the given positive number, mistakenly picking top-left without noticing how tightly clustered it is ( r would need to be close to 0.95 ).
  • Ignoring the positive sign: Forgetting that a negative slope means r < 0 , leading to picking the bottom-left plot because its scatter amount looks right.

Topics

Statistics · L: Data presentation and interpretation

Question and mark scheme from the AQA A-Level Mathematics examination, Paper 3, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.