Interpolation, extrapolation, and validity
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Question
Define interpolation.
Answer
Using a model to predict a value for an input that is within the range of the original data. Generally reliable.
Question
Define extrapolation.
Answer
Using a model to predict a value for an input that is outside the range of the original data. Less reliable — the pattern may not continue.
Question
Data collected 2010–2020. You predict the value in 2025. Is this interpolation or extrapolation?
Answer
Extrapolation — 2025 is beyond the end of the data range.
Question
Which is generally more reliable — interpolation or extrapolation? Why?
Answer
Interpolation — we stay within the range where the model was built and validated. Extrapolation assumes the pattern continues, which may not hold in new conditions.
Question
IB asks "Is your estimate reliable? Give a reason." The x-value is within the data range. How do you answer?
Answer
"Yes, the estimate is reliable as the value x = [n] is within the data range (interpolation)."
Question
IB asks "Is your estimate reliable?" The x-value is outside the data range. How do you answer?
Answer
"The estimate is less reliable as the value x = [n] is outside the data range (extrapolation). The model may not hold beyond the collected data."
Question
A linear model predicts a negative population for t = 100. What does this show?
Answer
The model breaks down for large t — populations cannot be negative. The model is only valid within the original data range.
Question
Why might predictions far into the future be unreliable even with a good model?
Answer
Conditions change over time (resources, policy, environment). The model was built on past data and assumes the same pattern continues indefinitely.
Question
What is the "valid domain" of a model?
Answer
The range of input values for which the model produces meaningful, realistic outputs — usually the range of the original data.
Question
h(t) = −5t² + 20t gives a ball's height. h(5) = −25. Why is this not valid?
Answer
Negative height is physically impossible — the ball has already hit the ground. The model is only valid for 0 ≤ t ≤ 4 (while airborne).
Question
How do you check whether a model output is "sensible"?
Answer
Ask: Is the output physically possible? Is the input within the data range? Does the result make sense in the context (correct units, realistic magnitude)?
Question
IB asks "State one limitation of this model." What kind of answer is expected?
Answer
One reason the model may not be perfectly accurate, e.g. "The model assumes constant growth rate, but this may not hold over long periods as conditions change."
Question
What is the IB-style format for answering "Is this estimate reliable?"
Answer
Yes/No + one reason referencing whether the input is within or outside the data range (interpolation vs extrapolation).
Question
Data collected for 0 ≤ t ≤ 10. You predict at t = 8. Write your reliability comment.
Answer
"The estimate is reliable as t = 8 is within the data range (interpolation)."
Question
Data collected for 0 ≤ t ≤ 10. You predict at t = 15. Write your reliability comment.
Answer
"The estimate is less reliable as t = 15 is outside the data range (extrapolation). The model may not hold beyond the collected data."
Question
IB asks "Suggest one reason why the model may not be appropriate." Give a strong example answer.
Answer
"The model assumes exponential growth continues indefinitely, but in reality growth may slow due to limited resources or carrying capacity."
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