The big idea: Interpolation: predicting y for an x-value that is inside the range of the data collected. More reliable — the model is supported by data in that region.
Extrapolation: predicting y for an x-value that is outside the range of the data. Less reliable — the pattern may not hold beyond the data.
| Term | Definition | Reliability |
|---|---|---|
| Interpolation | Prediction within the data range | Generally reliable — supported by data |
| Extrapolation | Prediction beyond the data range | Less reliable — model may not hold |
Interpolation
- Prediction is inside the data range
- Generally reliable — data supports it
- Example: data for t = 1 to 10; predict at t = 6
Extrapolation
- Prediction is outside the data range
- Less reliable — pattern may not hold
- Example: data for t = 1 to 10; predict at t = 25
Know the boundary: IB questions often ask whether a prediction is interpolation or extrapolation.
State the data range, then compare the prediction point to that range.
Example: 'Data covers ages 10–18.
Predicting at age 25 is extrapolation — less reliable.'
The big idea: Beyond the data range, the real-world pattern may change.
A linear model may stop being linear; a growth model may reach a natural limit.
The further you extrapolate, the less confidence you can have.
Evaluating reliability of a prediction
A linear model for a tree's height H (cm) against age t (years) is H = 15t + 20, based on data for t = 1 to 10.
A student uses this to predict height at t = 50.
Is this reliable?
Step by step
- Identify the data range.
- Identify the prediction point.
- Apply the model.
- Evaluate reliability.
Final answer
The prediction H = 770 cm is extrapolation and unreliable. Growth rate is unlikely to stay constant for 50 years.
Give a real reason: When evaluating reliability, do not just say 'it is extrapolation.' Explain why the pattern might change — e.g. 'trees slow their growth as they mature', 'the exponential growth cannot continue indefinitely.'
Practice with real exam questions
Answer exam-style questions and get AI feedback that shows you exactly what examiners want to see in a full-marks response.
The big idea: Every model has limitations — it is a simplification of reality.
A model may be valid over a limited domain but give unrealistic results outside it (negative populations, speeds above light, etc.).
Always check whether the output makes physical sense.
Questions to evaluate model validity
- Is the predicted value physically possible? (Can it be negative? Too large?)
- Is the x-value within or beyond the data range? (Interpolation or extrapolation?)
- Does the model type match the real-world behaviour over the full range?
- Are there natural limits the model ignores? (e.g. carrying capacity, physical maximum)
Always state domain restrictions: When describing a model, state the domain over which it is valid.
IB rewards 'the model is valid for 0 ≤ t ≤ 20' — this shows you understand the model has boundaries.
Critiquing a prediction — validity comment in IB style
A plant-growth study fits the model H(w) = 2.4w + 1.5 (height H in cm, week w) from data for weeks 1 to 10.
A student uses the model to predict H at week 50.
Write a validity comment for this prediction.
Step by step
- Identify the data range. The model was built on weeks 1 to 10 — that is the interpolation zone.
- Week 50 is FAR outside this range — this is extrapolation.
- Real plants slow their growth and eventually stop (biological limit). A purely linear model will keep increasing indefinitely, which is unrealistic for week 50.
- Write the validity comment combining the extrapolation flag AND the physical reason.
Final answer
The prediction at week 50 is extrapolation — it lies well outside the data range (weeks 1–10). Plants generally slow their growth and reach a mature height, so a linear model is unlikely to remain valid at this stage. The predicted height should be treated with caution and is not reliable.
The big idea: IB exam questions often ask whether a prediction is 'reliable' or 'valid'.
A good answer has three parts: (1) state whether it is interpolation or extrapolation, (2) say whether the result seems realistic, (3) give a contextual reason why the model may or may not hold.
Weak answer
- 'It is extrapolation so it is not reliable.'
- (No explanation, no context, no check of the result)
Strong answer
- 'The prediction is at t = 60, beyond the data range of t = 0 to 40 — this is extrapolation.'
- 'The model gives P = 12000, which seems unrealistically high for this city.'
- 'Population growth may slow due to limited resources, so the exponential model is unlikely to hold at t = 60.'
Three-part structure: For a validity question: (1) interpolation or extrapolation?
(2) Is the number realistic?
(3) Why might the model break down in context?