Scatter Graphs
Scatter graphs show the relationship between two variables. Each point represents one pair of values, such as revision time and test score.
A scatter graph helps you describe correlation and make estimates using a line of best fit.
Plotting points on a scatter graph
Each data pair is plotted as a point. The first value usually goes on the horizontal axis, and the second value goes on the vertical axis.
Example 1: Plotting a point
A student revises for 3 hours and scores 52 marks.
This is written as the coordinate:
(3, 52)
Plot 3 on the horizontal axis and 52 on the vertical axis.
Types of correlation
Correlation describes the pattern in the points. In GCSE Maths, you usually describe correlation as positive, negative, or no correlation.
Positive correlation: as one variable increases, the other tends to increase.
Negative correlation: as one variable increases, the other tends to decrease.
No correlation: there is no clear relationship.
Example 2: Describe the correlation
A scatter graph compares revision time and test score. The points go upwards from left to right.
This means students who revise for longer tend to score higher marks.
This is positive correlation.
Line of best fit
A line of best fit is drawn through the middle of the points. It should follow the trend, with roughly the same number of points on each side.
Example 3: Using a line of best fit
A line of best fit shows that a student who revises for 4 hours is expected to score about 65 marks.
This is an estimate, not an exact value.
Interpolation and extrapolation
Interpolation means estimating inside the range of the data. Extrapolation means estimating outside the range of the data.
Interpolation: usually more reliable.
Extrapolation: less reliable because it goes beyond the data collected.
Example 4: Interpolation or extrapolation?
A scatter graph has data for students who revised between 1 and 6 hours.
Estimating the score for 4 hours is interpolation because 4 is inside the data range.
Estimating the score for 9 hours is extrapolation because 9 is outside the data range.
A common mistake is saying that correlation proves one thing causes another. Scatter graphs show association, but they do not prove causation.
When describing correlation, mention both the direction and the context. For example: “There is positive correlation, so students who revise for longer tend to score higher marks.”
Video explanation
A short Worthing Maths Tutor video explanation for scatter graphs can be embedded here later to improve student engagement and time on page.
Practice questions
- A point represents 5 hours of revision and 71 marks. Write the coordinate.
- Points go upwards from left to right. What type of correlation is shown?
- Points go downwards from left to right. What type of correlation is shown?
- A graph has data from ages 10 to 16. Is estimating for age 14 interpolation or extrapolation?
- A graph has data from ages 10 to 16. Why might estimating for age 25 be unreliable?
Answers
- (5, 71)
- Positive correlation
- Negative correlation
- Interpolation
- It is extrapolation because age 25 is outside the data range.
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