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.__LINEBREAK___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.
Try Practice Free7-day free trial • No card required
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.
Worked example
Apply the key method from Interpolation, extrapolation, and validity in a typical IB-style question.
Step by step
- Write the relevant formula or rule first.
- Substitute values carefully and show each step.
- State the final answer with correct units/context.
Final answer
Clear method and context-based interpretation secure most marks.
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?