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A scatter graph plots two numerical variables, and correlation can be positive, negative or none. Free notes with worked examples and 14 questions answered.
Scatter Graphs and Correlation is part of Scatter Graphs and Correlation in GCSE AQA Higher Maths.
3 min
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11
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GCSE AQA Higher
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A scatter graph plots two numerical variables, and correlation can be positive, negative or none. Free notes with worked examples and 14 questions answered.
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Use this lesson to stay inside Scatter Graphs and Correlation while connecting the detail back to the wider Statistics topic.
Read the core explanations from Scatter Graphs and Correlation before testing yourself from memory.
A scatter graph is used when you have two numerical variables linked to the same item. Each point shows one pair of values. The overall shape of the cloud of points tells you whether the variables appear to be connected, and if they are, whether the connection is positive, negative or weak.
Typical GCSE examples compare things like revision time and test score, age and height, or engine size and fuel consumption. The key idea is that we are not listing one variable in isolation. We are studying how two measurements change together.
Strength matters as well as direction. If the points lie close to an imagined straight line, the correlation is strong. If the points are widely spread, the correlation is weak. Examiners often ask for both ideas together, for example 'strong negative correlation'.
| Pattern | What you should say | What you should avoid saying |
|---|---|---|
| Rises left to right | positive correlation | the graph proves one causes the other |
| Falls left to right | negative correlation | the graph means the variables must always move together |
| No clear trend | no correlation | there is definitely no relationship of any kind |
A scatter graph suggests a relationship. It does not prove a reason for that relationship. This distinction is vital. Two things can be correlated because one affects the other, because a third factor affects both, or simply by coincidence.
Worked example: Interpreting a scatter graph
A class records the number of hours revised in a week and the score in a test. The plotted points rise from left to right and lie fairly close to a straight line. Describe the correlation.
Answer: Strong positive correlation.
Suppose a scatter graph shows that ice cream sales and sunburn cases both increase on the same days. That does not mean ice cream causes sunburn. The hidden factor is sunny weather, which affects both variables. This is the standard GCSE caution when you are asked whether one variable causes the other.
Strong answers are short and precise: state the direction, comment on the strength, then deal with causation separately if the question asks for it. That structure is accurate, efficient, and exam-ready.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
The types of correlation on a scatter graph are positive, negative and no correlation. In positive correlation, as one variable increases the other tends to increase; in negative correlation, as one increases the other tends to decrease; and with no correlation there is no clear trend in the plotted points.
A scatter graph is used when there are two numerical variables linked to the same item, with each point showing one pair of values. The overall shape of the cloud of points shows whether the variables appear to be connected, and whether the connection is positive, negative or weak.
Positive correlation means that as one variable increases, the other tends to increase. On a scatter graph the points rise from left to right, as with hours revised in a week and test score.
Negative correlation means that as one variable increases, the other tends to decrease. On a scatter graph the points fall from left to right. It should not be described as meaning the variables must always move together.
Correlation is strong when the points lie close to an imagined straight line and weak when the points are widely spread. Strength depends on spread, not steepness, so strong correlation should not be confused with a steep gradient.
A scatter graph is interpreted by stating the direction of the correlation, commenting on its strength, and then dealing with causation separately. Points rising left to right show positive correlation, and points lying close to an imagined straight line show strong correlation, giving a conclusion such as strong positive correlation between revision hours and test score.
Correlation describes the relationship between two variables shown on a scatter graph. It can be positive, negative or no correlation, and it is described by its direction and its strength, for example strong negative correlation.
To describe correlation, state the direction and comment on the strength, for example 'strong positive correlation between revision hours and test score'. Points rising from left to right show positive correlation, and points lying close to a straight line show strong correlation. Deal with causation separately if asked.
Correlation does not mean causation: a scatter graph suggests a relationship but does not prove a reason for it. Ice cream sales and sunburn cases both increase on the same days, but ice cream does not cause sunburn; the hidden factor is sunny weather, which affects both variables.
A scatter graph with no correlation shows no clear trend in the plotted points. This is described as no correlation, not as proof that there is definitely no relationship of any kind between the two variables.
Strong correlation is not the same as a steep gradient. The strength of correlation depends on how spread out the points are, not on how steep the trend is. Points close to an imagined straight line show strong correlation, while widely spread points show weak correlation.
Two variables can be correlated because one affects the other, because a third factor affects both, or simply by coincidence. Ice cream sales and sunburn cases both rise on the same days, but ice cream does not cause sunburn; the hidden factor is sunny weather, which affects both.
A third variable is a hidden factor that affects both variables on a scatter graph, so they are correlated without one causing the other. Sunny weather is the third variable behind ice cream sales and sunburn cases rising together. If a third variable is plausible, it should be mentioned explicitly when discussing causation.
An outlier should be mentioned when describing a scatter graph if there is one. A strong answer names the correlation properly, comments on its strength, mentions any outlier, and deals with causation separately if the question asks for it.