Scatter Graphs & Correlation

 

What Is Correlation?

Correlation describes how two sets of data are connected.

Types of Correlation:

 

Types of Correlation	Description	Example
Positive	As one value increases, the other increases too	Height and shoe size
Negative	As one value increases, the other decreases	Time spent watching TV and exam scores
No correlation	No clear pattern or relationship	Favourite colour and number of pets

 

 

 

 

Important: Correlation $\not =$ Causation

Just because two things go up or down together doesn’t mean one causes the other.

Example:

As the number of ice creams sold increases, so do the number of people sunbathing.

✅ Correlation

❌ But buying ice cream doesn’t cause sunbathing — they’re both caused by hot weather!

 

What Is a Scatter Graph?

A scatter graph is a visual way of seeing if two sets of data are connected.

Each point represents one pair of values.

• X-axis: one variable (e.g. revision hours)
• Y-axis: the other variable (e.g. test scores)

We don’t join the points — we just look at the pattern they make.

 
What Do the Patterns Look Like?

 

Pattern	Meaning
Rises from bottom left to top right	Positive correlation
Falls from top left to bottom right	Negative correlation
No clear shape	No correlation
Points close to a straight line	Strong correlation
Points scattered further from the line	Weak correlation

 

Example

A science teacher records how long 10 students revise and the marks they get in a quiz:

 

Hours Revised	Quiz Mark (%)
1	35
2	40
3	47
4	52
5	60
6	66
7	70
8	76
9	82
10	88

 

(a) Draw a scatter graph

• Plot each pair of values (e.g. (1, 35), (2, 40), …).
• Use crosses and do not join them up.

(b) Describe the correlation

As the number of hours revised increases, the quiz mark increases too.

This is strong positive correlation.

(c) Can you say that revising more caused the higher marks?

Not exactly!

There may be other factors, like natural ability or sleep.

So we say: “There is a correlation, but this does not prove causation.”