Reading & writing · Grades 10–12
Beyond the tested range
Read once, answer together, and check your reasoning.
Beyond the tested range
A cooling model is fitted to measurements from 20 to 60 minutes after an object is removed from a warm enclosure. Its predictions match the observed interval closely. A report then uses the same formula to estimate the object’s temperature days later without checking environmental changes or the model’s assumptions. The analyst distinguishes interpolation within the fitted interval from extrapolation far beyond it.
Try it yourself
What is the difference between interpolation and extrapolation in this passage?
Why does a close fit within the interval not guarantee accuracy days later?
Name one assumption that should be checked before the long-range prediction.
How should the report communicate the long-range estimate?
Check your understanding
Answers and marking notes
- Interpolation estimates within the observed interval; extrapolation estimates outside it.
Interpolation estimates within the observed interval; extrapolation estimates outside it.
- Conditions may change and the mathematical relationship may not remain valid outside the tested range.
Conditions may change and the mathematical relationship may not remain valid outside the tested range.
- Accept stable surroundings, a suitable heat-transfer model, no phase change or other relevant physical condition.
Accept stable surroundings, a suitable heat-transfer model, no phase change or other relevant physical condition.
- State it as conditional on assumptions, identify the extrapolation and uncertainty, and avoid presenting it as verified fact.
State it as conditional on assumptions, identify the extrapolation and uncertainty, and avoid presenting it as verified fact.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.