A line of best fit summarises the trend in a scatter graph by passing as close as possible to all the plotted points. Read it like a conversion graph to predict unknown values. Predictions within your data range (interpolation) are reliable; those outside it (extrapolation) are uncertain.
What is a line of best fit?
A line of best fit (also called a trend line) is a straight line drawn through a scatter diagram so that:
- The points are distributed roughly evenly on either side of the line.
- The total distance from the points to the line is as small as possible overall.
- It passes through or near the mean point (x̄, ȳ) — the point formed by the mean of the x-values and the mean of the y-values.
It is not a dot-to-dot line — you draw one single straight line, not a zig-zag through every point.
How do you draw a line of best fit?
Follow these four steps:
- Check there is a correlation. A line of best fit is only meaningful when there is a visible pattern (positive or negative correlation). For no correlation, a line of best fit conveys false information.
- Find the mean point (x̄, ȳ). Calculate the mean of all x-values and the mean of all y-values. Mark this point on the graph with a cross.
- Draw a straight line through or near the mean point so that roughly half the data points are above the line and half are below.
- Extend to the edges of the plotted data, but no further — unless making an extrapolation that you flag as uncertain.
How do you use the line to make predictions?
Example: a scatter graph shows the relationship between revision hours (x-axis) and test scores (y-axis). The line of best fit is drawn.
To predict the test score for 7 hours of revision:
- Find 7 on the x-axis.
- Draw a vertical line up to the line of best fit.
- Draw a horizontal line across to the y-axis.
- Read off the predicted score.
To predict the revision hours needed for a score of 75:
- Find 75 on the y-axis.
- Draw a horizontal line across to the line of best fit.
- Draw a vertical line down to the x-axis.
- Read off the revision hours.
Always show the construction lines on the graph — exam marks are awarded for the method, not just the reading.
What is the difference between interpolation and extrapolation?
| Type | Definition | Reliability |
|---|---|---|
| Interpolation | Predicting a value within the range of the data | Generally reliable — the trend is established in this range |
| Extrapolation | Predicting a value outside the range of the data | Unreliable — the trend may not continue beyond the data |
Example: data covers revision hours from 2 to 10. Predicting for 7 hours is interpolation (7 is within 2–10) — reliable. Predicting for 15 hours is extrapolation — the relationship may not hold, and the prediction should be flagged as unreliable.
What if there is no correlation?
If the scatter diagram shows no correlation (points scattered randomly), a line of best fit cannot reliably be drawn and predictions from it are meaningless. The question may still ask you to explain why prediction is not appropriate — state clearly that there is no correlation.
For a weak correlation, predictions have greater uncertainty. For a strong correlation, predictions will be closer to the true value.
Common exam errors to avoid
- Drawing a line from the origin (0, 0) unless the data supports this. The line of best fit is drawn from the data, not forced through the origin.
- Not passing the line through the mean point. Many students draw a line that looks roughly right but misses the mean point, making all predictions slightly off.
- Reading the wrong axis. When asked to predict a y-value, go from the x-axis to the line and then across — not the other way round. Label which direction you are going if it helps.
- Extrapolating without acknowledging the risk. Any prediction outside the data range should be accompanied by a note that it is uncertain.
Frequently asked questions
Does the line of best fit have to pass through the mean point?
Not exactly — in a GCSE exam you are not expected to calculate the mean point precisely, but your line should pass through or very close to it. Calculating the mean point and plotting it before drawing the line is good practice and makes a stronger answer.
Can the line of best fit have a negative gradient?
Yes. A negative gradient indicates a negative correlation — as one variable increases, the other decreases. For example, the more absences from school, the lower the test score. Draw the line from upper left to lower right rather than lower left to upper right.
How precise should my reading from the line be?
Read to the nearest scale division you can reasonably identify. State your answer clearly with the correct unit and a suitable degree of accuracy. Most GCSE mark schemes accept a small range of values for the reading — typically ± 1 or 2 units.
Is the line of best fit the same as the equation of the trend line?
The line of best fit on a scatter graph is a graphical representation. Its gradient and y-intercept give the equation y = mx + c, which is the trend line equation. GCSE questions sometimes ask for the equation — find two points on the line (not data points) and calculate m = (y₂ − y₁)/(x₂ − x₁), then find c.
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