GCSE MATHS • HIGHER TIER
Line of Best Fit Made Simple
Draw balanced trend lines, use scatter graphs and make reliable estimates from correlated data.
Clear method
Exam practice
Worked proofs
Line of Best Fit in Four Moves
1
Plot
Plot the paired data accurately on a scatter graph.
2
Identify the Trend
Decide whether the data shows positive, negative or no correlation.
3
Draw
Use a ruler to draw a straight line through the middle of the points, with roughly equal numbers above and below.
4
Predict
Read estimates from the line and judge whether interpolation or extrapolation is being used.
What You’ll Learn
Understand what a line of best fit represents.
Recognise when a line of best fit should be used.
Draw a balanced line of best fit.
Use the line to estimate unknown values.
Understand interpolation and extrapolation.
Handle outliers correctly when drawing the line.
Key Rules
Use a line of best fit only when the scatter graph shows clear correlation.
Draw one straight line through the middle of the points.
Use a ruler to draw the line accurately.
Keep roughly equal numbers of points above and below the line.
The line does not need to pass through every point.
Worked Proof: Line of Best Fit
Step-by-Step Method
- 1. Plot the paired data accurately on a scatter graph.
- 2. Identify whether the correlation is positive, negative or absent.
- 3. Check that the relationship is strong enough for a line of best fit.
- 4. Ignore any obvious outliers.
- 5. Use a ruler to draw a balanced line through the middle of the points.
More Worked Examples
1
Question : A scatter graph shows revision hours against exam scores. The points rise from left to right.
Answer : Draw an upward-sloping line of best fit.
2
Question : A scatter graph shows speed against journey time. The points fall from left to right.
Answer : Draw a downward-sloping line of best fit.
3
Question : A line of best fit passes through the point where 6 hours of revision corresponds to approximately 70%. Estimate the score for 8 hours of revision.
Using the line, the estimate is approximately 78%.
Answer : 78%
4
Question : A scatter graph shows no correlation.
Answer : Do not draw a line of best fit.
- Common GCSE Mistakes
- Forcing the line through every point.
- Drawing a line of best fit when there is no correlation.
- Letting an outlier distort the overall trend.
- Confusing interpolation with extrapolation.
- Exam Tips
- Check that there is clear positive or negative correlation first.
- Use a ruler and draw one straight trend line.
- Aim for roughly equal numbers of points above and below the line.
- Ignore obvious outliers when judging the main trend.
- Read predictions from the line rather than from individual points.
- Remember that extrapolation is less reliable than interpolation.e line rather than from individual points.
Skills Used in Line of Best Fit
Scatter Graphs
Correlation
Line of Best Fit
Interpolation
Extrapolation
Outliers
Predictions
Statistical Interpretation
Ready to Practise?
Printable Worksheet
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Interactive Quiz
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Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Line of Best Fit Tutorial
Step-by-step walkthroughs of Line of Best Fit with clear methods and exam tips.
Frequently Asked Questions
It is a straight line drawn through the middle of points on a scatter graph to represent the overall trend.
Use it when there is clear positive or negative correlation. The source says it is not useful when there is no correlation.
It should pass through the middle of the points with roughly equal numbers above and below it.
Interpolation is making a prediction within the range of the existing data.
Extrapolation is predicting outside the data range and is less reliable because the trend may not continue.
The source says obvious outliers should usually be ignored when drawing the line of best fit because they do not follow the general trend.