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 covers each concept with clear examples. For an overview of every topic, see our complete GCSE Maths topics list.

What Is Correlation?

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.

Types of Correlation

• 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.

Strength of Correlation

• 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.

Key Formulas

There is no numerical calculation required at GCSE for correlation — you describe it from the scatter graph. At Higher level, you may be asked to interpret the context.

Step-by-Step Method

1. Look at the overall pattern of the scatter graph.
2. Determine the direction: do the points rise (positive), fall (negative), or show no trend?
3. Assess the strength: are the points tightly clustered (strong) or widely spread (weak)?
4. Describe the correlation in context, e.g. "There is a strong positive correlation between hours of revision and test score."
5. If appropriate, draw a line of best fit through the middle of the data.
6. Use the line to estimate values — noting whether you are interpolating or extrapolating.

Worked Example 1 — Foundation Level

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.

Working:

The points fall from left to right, so the correlation is negative. They are closely grouped, so it is strong.

Answer: There is a strong negative correlation — as temperature increases, the number of hot drinks sold decreases.

Worked Example 2 — Higher Level

Question: A line of best fit on a scatter graph passes through the points (10, 30) and (50, 70). (a) Estimate y when x = 25. (b) Estimate y when x = 80. (c) Which estimate is more reliable? Explain.

Working:

(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.

(c) The estimate for x = 25 is more reliable because 25 is within the range of data (interpolation). The estimate for x = 80 is extrapolation — it is outside the data range, and the trend may not continue.

Answer: (a) 45, (b) 100, (c) x = 25 is more reliable (interpolation within the data range).

Worked Example 3 — Exam Style

Question: A student finds a strong positive correlation between ice cream sales and drowning incidents. She concludes that eating ice cream causes drowning. Is she correct?

Working:

The student is not correct. Correlation does not prove causation. Both ice cream sales and drowning incidents increase during hot weather — the common factor is temperature. The ice cream does not cause the drowning.

Answer: Incorrect. Correlation does not imply causation — a third variable (hot weather) causes both to increase.

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.

Practice Questions

Q1 (Foundation): A scatter graph shows points rising from left to right. Describe the type of correlation.

Q2 (Foundation): What is meant by "no correlation"?

Q3 (Higher): A scatter graph shows data for x = 5 to x = 30. A student uses the line of best fit to estimate y when x = 50. Comment on the reliability of this estimate.

Practise identifying correlation and using lines of best fit free on GCSEMathsAI.

Related Topics

• Scatter Graphs and Correlation
• Finding the Mean
• Finding the Median

Summary

• Correlation describes the relationship between two variables on a scatter graph: positive (both increase), negative (one increases as the other decreases), or none.
• Strength is described as strong, moderate or weak depending on how closely points cluster around a line.
• A line of best fit follows the overall trend and can be used to estimate values.
• Interpolation (within the data range) is reliable; extrapolation (outside it) is not.
• Correlation does not prove causation — always consider whether a third factor could explain the relationship.