The mean point, denoted as , is the mathematical 'center' of the data set and serves as the anchor for the line of best fit.
To calculate the coordinates, find the arithmetic mean of all -values and all -values separately:
A mathematically accurate line of best fit must pass through this mean point if it has been calculated or provided.
| Feature | Interpolation | Extrapolation |
|---|---|---|
| Definition | Predicting values within the range of existing data. | Predicting values outside the range of existing data. |
| Reliability | High; the trend is supported by surrounding data. | Low; the trend may not continue indefinitely. |
| Method | Reading from the line between the first and last points. | Extending the line beyond the plotted data points. |
Interpolation is generally considered safe because it assumes the established relationship holds true between known observations.
Extrapolation is risky because external factors might change the relationship outside the observed window (e.g., a growth trend might level off).
Always use a ruler: Freehand lines are inaccurate and will likely lose marks in a formal assessment.
Check the Mean Point: If a question asks you to calculate the mean point, the examiner is specifically checking if your line passes through that exact coordinate.
Range of Acceptance: Examiners usually allow a small margin of error for the gradient, but the line must clearly follow the 'balance' rule (equal points on either side).
Prediction Accuracy: When asked to estimate a value, draw dashed lines from the axis to the line of best fit and then to the other axis to show your working clearly.
