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Interpolation estimates a value inside the plotted data using the line of best fit, and extrapolation estimates outside it. 13 questions answered.
Lines of Best Fit, Interpolation and Extrapolation is part of Scatter Graphs and Correlation in GCSE AQA Higher Maths.
2 min
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11
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GCSE AQA Higher
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Interpolation estimates a value inside the plotted data using the line of best fit, and extrapolation estimates outside it. 13 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 Lines of Best Fit, Interpolation and Extrapolation before testing yourself from memory.
Once a scatter graph shows a clear trend, the next step is often to draw a line of best fit. This line captures the overall direction of the points so that you can estimate unknown values. It should pass through the middle of the data with roughly the same number of points on each side.
A line of best fit is not drawn through every point. It is a balancing line. If one point is clearly far away from the trend, it may be an outlier and should not control the whole line.
Interpolation is usually more reliable because it stays inside the pattern supported by the data. Extrapolation is riskier because the trend may stop, flatten, or change beyond the values observed.
Worked example: Estimating from a line of best fit
A scatter graph compares temperature and daily ice cream sales. A line of best fit has been drawn. Estimate the number of ice creams sold when the temperature is 24°C, and explain whether this is interpolation or extrapolation.
Answer: About 78 sales; interpolation if 24°C is inside the original data range.
An outlier is a point that sits well away from the general pattern. It could be caused by a mistake in recording data, a special circumstance, or natural unusual variation. In an exam answer, it is good practice to mention an outlier if it affects the reliability of your prediction.
| Situation | How reliable is the estimate? | Why? |
|---|---|---|
| Interpolation on a strong trend | Quite reliable | The estimate sits inside the observed pattern. |
| Interpolation with an outlier nearby | Reasonably reliable | The main pattern still helps, but the unusual point should be noted. |
| Extrapolation far beyond the data | Less reliable | The trend may not continue outside the observed range. |
Scatter graph questions reward clear statistical language more than long explanations. Draw the line carefully, read the axes accurately, and justify reliability in one precise sentence.
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-03-21.
Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
To draw a line of best fit, check the scatter graph has a clear trend, ignore any obvious outlier, then draw a straight line through the centre of the points. It should pass through the middle of the data with roughly the same number of points on each side, not through every point.
Interpolation is using the line of best fit to estimate a value inside the range of data already plotted. Reading the likely score for 6 hours of revision when a graph covers 2 to 10 hours is interpolation, and it is usually more reliable because it stays inside the pattern supported by the data.
Extrapolation is using the line of best fit to estimate a value outside the range of data already plotted. Predicting the score for 15 hours of revision when a graph only covers 2 to 10 hours is extrapolation, and it is riskier because the trend may stop, flatten or change.
Interpolation uses the line of best fit to estimate a value inside the range of data already plotted, while extrapolation estimates a value outside that range. Interpolation is usually more reliable; extrapolation is riskier because the trend may stop, flatten, or change beyond the values observed.
Extrapolation is less reliable because it estimates values outside the observed range, where the trend may not continue. For example, predicting the score for 15 hours of revision when the graph only covers 2 to 10 hours is riskier, as the trend may stop, flatten, or change.
To estimate with a line of best fit, find the known value on the horizontal axis, move up to the line, then read across to the vertical axis. For example, reading up from 24°C might give about 78 ice cream sales, which is an estimate, so a sensible rounded value is acceptable.
An outlier is a point that sits well away from the general pattern on a scatter graph. It could be caused by a mistake in recording data, a special circumstance, or natural unusual variation, and it should not control the whole line of best fit.
A line of best fit is not drawn through every point; it is a balancing line. It should pass through the middle of the data with roughly the same number of points on each side, and an obvious outlier should not control the whole line.
An obvious outlier should be ignored when judging the overall direction for a line of best fit, so that it does not control the whole line. An outlier is a point well away from the general pattern, and it should be mentioned if it affects the reliability of a prediction.
An outlier on a scatter graph can be caused by a mistake in recording data, a special circumstance, or natural unusual variation. It is a point that sits well away from the general pattern of the other points.
An estimate from a line of best fit is quite reliable when it is interpolation on a strong trend, because it sits inside the observed pattern. Interpolation with an outlier nearby is reasonably reliable, but extrapolation far beyond the data is less reliable because the trend may not continue outside the observed range.
A line of best fit is used to capture the overall direction of the points on a scatter graph so that unknown values can be estimated. It is drawn once a scatter graph shows a clear trend, as a straight line through the centre of the points.
An estimate is interpolation if the value used lies within the original data range, and extrapolation if it lies outside it. For example, an estimate of about 78 ice cream sales at 24°C is interpolation if 24°C is inside the plotted temperature range.