A scatter diagram shows the relationship between two paired variables. By studying the pattern of points, it is possible to describe the type of relationship and draw sensible conclusions from the data.

 

 

Describing Correlation

The term correlation describes how two variables are related.

 

There are three main types of correlation used at GCSE level.

 

 

Positive correlation

This occurs when, as one variable increases, the other variable also tends to increase.

 

On a scatter diagram, the points generally slope upwards from left to right.

 

For example, as time spent revising increases, test score may increase.

 

 

Negative correlation

This occurs when, as one variable increases, the other variable tends to decrease.

 

On a scatter diagram, the points generally slope downwards from left to right.

 

For example, as speed increases, journey time may decrease.

 

 

Little or no correlation

This occurs when there is no clear relationship between the variables.

 

The points appear scattered with no clear upward or downward trend.

 

In this case, knowing the value of one variable gives little information about the other.

 

 

Strength of Correlation

Correlation can be:
• strong
• weak

 

A strong correlation has points close to a straight line.

 

A weak correlation has points more widely spread, even though a general trend may still be visible.

 

The closer the points are to a line of best fit, the stronger the correlation.

 

 

Interpreting Scatter Diagrams

When interpreting a scatter diagram, you should:
• describe the type of correlation
• comment on how strong it appears
• mention any anomalies
• link conclusions to the data shown

 

For example, you might state that there is a positive correlation because values tend to increase together.

 

An anomaly is a point that does not fit the general pattern. Anomalies should be mentioned and considered when drawing conclusions.

 

 

Drawing Conclusions

Conclusions should:
• be based on the overall trend
• use correct statistical language
• avoid claiming cause and effect

 

A scatter diagram can show association, but it does not prove that one variable causes the other to change.

 

Always be cautious and realistic when interpreting results.

 

Correlation does not imply causation

 

 

Common Errors to Avoid

Common mistakes include:
• confusing positive and negative correlation
• ignoring the overall trend
• focusing on one or two points only
• claiming cause and effect

 

Always describe what the data shows, not what you think caused it.

 

 

Key Points to Remember

Scatter diagrams show relationships between paired variables.
Positive correlation means both variables increase together.
Negative correlation means one increases as the other decreases.
Little or no correlation shows no clear relationship.
Conclusions must be based on trends and use correct terminology.

 

Being able to interpret scatter diagrams accurately allows relationships in data to be described clearly and conclusions to be drawn sensibly and correctly.