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MathidiaMathematics Academy
Statistical investigation
Lesson 64 of 75
Challenge

Scatter analysis

Objective. Interpret correlation and distinguish it from causation.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Scatter analysis examines a scatter graph to describe the correlation between two variables, which can be positive (both increase together), negative (one increases as the other decreases), or show no correlation at all. A line of best fit can be drawn through the data to summarise the trend and make predictions, but correlation alone does not prove one variable causes changes in the other. For example, ice cream sales and sunburn cases might show positive correlation, but the real cause is hot weather affecting both, not one causing the other. Recognising this difference between correlation and causation is essential when interpreting real data.

Worked example

A scatter graph shows that as the number of hours of sunshine increases, the number of cold drinks sold also increases. Explain why this does not necessarily prove causation.

y = mx + c
Coordinate grid with the line y = mx + c
  1. 1Identify the type of correlation shown: positive correlation, since both variables increase together.
  2. 2Consider whether a third factor could explain both trends.
  3. 3Hot temperature could cause both increased sunshine hours and the desire for cold drinks.
  4. 4Therefore the relationship may be due to a shared underlying cause, temperature, rather than direct causation.

Answer: Correlation shows a relationship but does not prove sunshine directly causes drink sales; temperature may cause both.

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Practice

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Common mistake. Pupils often conclude that a strong correlation on a scatter graph proves that one variable directly causes the other, without considering other explanations such as a shared underlying cause. Always state that correlation shows a relationship, not necessarily causation.

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