A-Level · Mathematics · AQA · Mark scheme decoded
AQA A-Level Mathematics: Interpreting Scatter Diagrams and Regression Lines — mark scheme explained
The short answer
Scatter diagrams, also known as scatter plots, are graphical representations used to display the relationship between two variables. They help in understanding how one variable changes with respect to another. In this section, we will explore how to interpret scatter diagrams, regression lines, and understand the concept of correlation without delving into complex calculations.
The question
A scatter diagram shows the relationship between the number of hours spent studying and exam scores for a group of students. The points form an upward-sloping pattern. What does this indicate? [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Examine the pattern of the data points on the scatter diagram.
- S2
Identify that the points form an upward-sloping pattern.
- S3
Conclude that there is a positive correlation between the number of hours spent studying and exam scores.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Examine the pattern of the data points on the scatter diagram.
- S2
Identify that the points form an upward-sloping pattern.
- S3
Conclude that there is a positive correlation between the number of hours spent studying and exam scores.
Final answer: There is a positive correlation between the number of hours spent studying and exam scores, indicating that as study time increases, exam scores tend to increase as well.
Common mistakes
- Assuming a positive or negative pattern when there is none — Carefully examine the data points and look for a clear upward or downward trend before concluding the type of correlation.
- Failing to recognize distinct sections in the scatter diagram — Look for any patterns or clusters that might indicate different subgroups and consider their implications.
- Confusing correlation with causation — Understand that correlation does not imply causation and consider potential confounding variables or underlying factors.
- Misinterpreting the strength of correlation — Consider the overall trend and distribution of data points to accurately assess the strength of the correlation.
- Failing to describe the direction of the correlation — Always specify whether the correlation is positive, negative, or absent when interpreting scatter diagrams.
- Not providing a clear conclusion — Ensure that your conclusions are clear, specific, and directly address the relationship between the variables.
Where the marks go
- Full worked solution (all marking points)3 marks