Sheet № 185 · Foundation + Higher · AQA · Edexcel · OCR
Types of Correlation –
Understanding correlation is essential for GCSE Maths and is tested on both Foundation and Higher papers across AQA, Edexcel and OCR. You need to identify positive, negative and no correlation, describe the strength of a relationship, draw and use a line of best fit, and distinguish between interpolation and extrapolation. This guide cove
§Key definitions
Correlation
describes the relationship between two variables shown on a scatter graph. It tells you whether the variables tend to increase together, whether one decreases as the other increases, or whether there is no obvious pattern.
Question:
A scatter graph plots temperature (horizontal) against number of hot drinks sold (vertical). The points fall from left to right and are closely grouped. Describe the correlation.
Answer:
There is a strong negative correlation — as temperature increases, the number of hot drinks sold decreases.
(a)
Gradient = (70 − 30) ÷ (50 − 10) = 40 ÷ 40 = 1. Using point (10, 30): y = 30 + 1 × (25 − 10) = 30 + 15 = 45.
(b)
y = 30 + 1 × (80 − 10) = 30 + 70 = 100.
§Formulas to memorise
Correlation describes the direction and strength of a linear relationship between two variables
Positive correlation — as one variable increases, the other increases. Points rise from left to right.
Negative correlation — as one variable increases, the other decreases. Points fall from left to right.
No correlation — there is no clear pattern between the two variables. Points are scattered randomly.
Strong — points cluster tightly around an imaginary straight line.
Weak — points roughly follow a trend but are more spread out.
Moderate — between strong and weak.
Worked example
A scatter graph plots temperature (horizontal) against number of hot drinks sold (vertical). The points fall from left to right and are closely grouped. Describe the correlation.
Working:
⚠ Common mistakes
- ✗Confusing correlation with causation. A correlation shows that two variables are related, but it does not prove that one causes the other.
- ✗Describing correlation without context. At Higher level, always relate the correlation to the variables in the question, not just say "positive" or "negative".
- ✗Extrapolating and treating it as reliable. Estimates made outside the range of data are unreliable. Always state this when extrapolating.
- ✗Drawing a line of best fit through the origin. The line should follow the data — it does not have to pass through (0, 0).
✦ Exam tips
- →Always use three elements when describing correlation: type (positive/negative/none), strength (strong/weak), and context (relate it to the variables).
- →If asked to compare reliability of estimates, check whether the value is within the data range (interpolation) or outside it (extrapolation).
- →If asked "Does this prove...?", the answer is almost always no — state that correlation does not prove causation.
- →For related topics, see scatter graphs and correlation. For key formulas, visit our GCSE Maths formulas page.