AQA AS Level Mathematics Paper 2, June 2025: Question 17

4 marks · Easy difficulty · Short Answer

Interpret a scatter diagram relating wind speed and raincoat sales to identify an outlier, assess the effect of removing it on the correlation coefficient, describe the correlation in context, and comment on causality.

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Question

Question text

17 The owner of a shop recorded the average daily wind speed in mph and the total sales

of raincoats in pounds over a period of 6 months.

The data from a random selection of 15 days from the 6‑month period is shown in the

scatter diagram.

Daily E G

sales of

raincoats H I

(£) 200

J K

L N

A M

05 10 15 20 25 30

Wind speed (mph)

One of the points on the scatter diagram is an outlier.

17 (a) State the letter from the diagram which corresponds to this outlier.

[1 mark]

17 (b) State the effect on the numerical value of the correlation coefficient if the

outlier was removed from the data.

[1 mark]

17 (c) Describe, in context, the correlation indicated by the scatter diagram.

[1 mark]

(20) …

17 (d) The owner of the shop claims that the scatter diagram proves that windier days cause

lower sales of raincoats.

Comment on the validity of this claim.

[1 mark]

Mark scheme

Show the mark scheme

Q Marking instructions AO Marks Typical solution

17(a) States A 2.2a B1 A

Subtotal 1

17(b) Explains that the value would

become more negative or strong 2.4 E1

The value would become more

negative OE

negative

Accept smaller/decrease

Subtotal 1

17(c) Describes the correlation in 2.2b E1 The higher the wind speed the

context. Require ‘sale(s)’ and lower the daily sales of raincoats

‘wind speed’ Do not accept

‘number’ /’amount’

Accept negative correlation (with

‘sale(s)’ and ‘wind speed’)

Do not accept ‘number’/’amount’

Subtotal 1

17(d) States claim is not valid OE, This claim is not valid. The scatter

with a comment; 2.2b E1 diagram cannot prove causality,

E.g. there could be another factor which

• Scatter diagram/correlation is causing the fall in sales, e.g.

cannot prove causality amount of rainfall

• Could be another factor for

drop in sales

• 15 days is a small sample

from a six-month period

Accept it may be valid but the

scatter diagram does not prove

it.

Subtotal 1

Question 17 Total 4

How to answer it

Bivariate Data: Scatter Diagrams, Correlation & Causality

WHAT THIS QUESTION TESTS

This question assesses your core statistical literacy across four foundational areas:

Outlier Identification: Locating anomalous observations that deviate strongly from the bivariate trend.
Effect on Correlation Coefficient (r): Understanding how the removal of an outlier shifts the numerical value of PMCC towards -1 or +1.
Contextual Interpretation: Describing a negative association using precise context variables (wind speed and sales of raincoats).
Correlation vs. Causality: Critiquing causal claims from observational bivariate data and suggesting confounding factors.

Part (a) — Identifying the Outlier

State the letter from the diagram which corresponds to this outlier [1 mark]

✅ Correct Answer

Mark: 1 × B1 (AO 2.2a) — Unambiguous identification of point A.

💡 Key Knowledge

An outlier in bivariate data is a point that falls well away from the overall linear pattern formed by the rest of the points. While most points lie along a clear downward slope from top-left (low wind, high sales) to bottom-right (high wind, low sales), point A (wind speed ≈ 1.5 mph, sales ≈ £85) sits drastically lower than expected.

Part (b) — Impact of Removing an Outlier on PMCC

State the effect on the numerical value of the correlation coefficient if the outlier was removed from the data [1 mark]

✅ Correct Answer

Any one of the following statements:

The value would become more negative
It would show a stronger negative correlation
The numerical value would decrease / become smaller (e.g. from -0.6 to -0.85)

Mark: 1 × E1 (AO 2.4) — Clear explanation of numerical change.

📐 Step-by-Step Logic Trap

The general data displays a negative correlation, meaning r < 0.
Point A weakens this negative linear relationship by pulling the line of best fit down near the origin.
Removing point A makes the negative linear association stronger.
Numerically, moving further in the negative direction means the value becomes more negative (decreases/gets smaller).

❌ Common Errors

Saying "it increases": Students confuse strength/magnitude (|r|) with numerical value. Moving from -0.5 to -0.85 is a decrease in numerical value, even though the strength has increased.
Omitting "negative": Simply writing "it gets closer to 1" without the minus sign loses the mark. It gets closer to -1.

🧠 Exam Technique

Look at the exact wording: "numerical value". For a negative correlation, stronger means more negative, which mathematically is a decrease. To avoid ambiguity, write: "The value becomes more negative (closer to -1)."

Part (c) — Interpreting Correlation in Context

Describe, in context, the correlation indicated by the scatter diagram [1 mark]

✅ Correct Answer

Any valid contextual interpretation linking both variables:

"As the wind speed increases, the daily sales of raincoats decrease" (or vice versa).
"There is a negative correlation between wind speed and sales of raincoats."

Mark: 1 × E1 (AO 2.2b) — Full context required.

💡 Mark Scheme Requirements

To secure the mark, the scheme strictly insists on:

Mentioning both "sales" (or raincoat sales) and "wind speed".
Correctly stating the direction (negative / as one increases, the other decreases).

❌ Common Errors

Vague terminology: Writing "the amount of raincoats" or "the number of raincoats" instead of sales (sales is measured in £). The mark scheme notes: Do not accept 'number' / 'amount'.
Leaving out context: Writing purely "negative correlation" without naming the variables receives 0 marks.

Part (d) — Evaluating Validity & Causality

The owner claims the scatter diagram proves that windier days cause lower sales of raincoats. Comment on the validity of this claim [1 mark]

✅ Correct Answer

State that the claim is not valid (or cannot be proven), accompanied by a valid reason:

Correlation does not imply causation: The scatter diagram shows association, not a causal link.
Confounding variables / other factors: Another factor could be driving the relationship (e.g. rainfall, temperature, or season).
Sample size limitation: 15 days is a very small sample taken from a 6-month period.

Mark: 1 × E1 (AO 2.2b) — "Not valid" + justified reasoning.

🧠 Exam Technique: The Golden Rule

Whenever an exam question asserts that correlation "proves" or "causes" something, your alarm bells should ring:

Start by clearly stating: "The claim is not valid."
Give the statistical justification: "Correlation does not imply causality."
Give a plausible confounding variable: "For instance, rain volume or season might be the underlying factor affecting sales."

Topics

Statistics · L: Data presentation and interpretation

Question and mark scheme from the AQA AS Level Mathematics examination, Paper 2, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.