Extrapolation is dangerous because it uses a model outside the range of observed data, where the relationship may change or the model's assumptions may no longer be valid. Consequently, predictions can become increasingly unreliable the further they extend beyond the data range.
This is part of SL 2.6: Modelling skills, studied at both SL and HL and applicable to Paper 1 short-response and Paper 2 extended-response questions.
Why extrapolation can fail
A mathematical model simplifies reality by assuming that an observed pattern continues. Interpolation estimates within the observed data range, while extrapolation predicts beyond it.
Suppose data are collected for years to , producing the linear model
where is a population in thousands. Predicting is interpolation, because is within the observed range. Predicting is extrapolation: the calculation is correct according to the model, but resource limits, migration, or changing growth rates may make the prediction unrealistic.
| Danger | Why it weakens the prediction |
|---|---|
| The relationship changes | Linear growth may become exponential, logistic, seasonal, or declining. |
| Model assumptions fail | Conditions that produced the original data may not continue. |
| Small model errors grow | A slight error in gradient or parameters can produce a large long-term error. |
| Impossible predictions occur | A model may predict negative quantities or values beyond physical limits. |
| Unusual events intervene | Policy changes, economic shocks, or environmental events may alter the trend. |
A common misconception is that a high coefficient of determination, such as , guarantees accurate future predictions. It only indicates how well the model explains variation in the observed data; it does not validate predictions outside that range.
Exam technique
If asked to comment on an extrapolated prediction, identify that the input lies outside the data range and give a contextual reason why the trend may not continue. Do not merely state that extrapolation is “inaccurate”; explain which assumption could fail and how this reduces the model's validity.
