Question
2- Choose the most correct statement from the options below:
a) Linear interpolation is always exact for any two data points, regardless of the actual
behaviour
b) Extrapolation beyond the table’s highest or lowest temperature can yield large errors
and should be avoided unless no other data exist.
c) Visual estimates (without a formula) are sufficient if the data do not vary drastically.
a) Linear interpolation is always exact for any two data points, regardless of the actual
behaviour
b) Extrapolation beyond the table’s highest or lowest temperature can yield large errors
and should be avoided unless no other data exist.
c) Visual estimates (without a formula) are sufficient if the data do not vary drastically.
Ask by Sherman Lynch. in Bahrain
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Extrapolation beyond the data range can lead to large errors and should be avoided unless no other data is available.
Solution
To determine the most correct statement from the options provided, let’s analyze each one:
a) Linear interpolation is always exact for any two data points, regardless of the actual behaviour.
- This statement is misleading. Linear interpolation assumes that the data between two points can be represented by a straight line. While it is exact for the two points used, it may not accurately represent the actual behavior of the data if the underlying relationship is nonlinear.
b) Extrapolation beyond the table’s highest or lowest temperature can yield large errors and should be avoided unless no other data exist.
- This statement is generally true. Extrapolation involves estimating values outside the range of known data, which can lead to significant errors, especially if the trend does not continue beyond the observed data. It is advisable to avoid extrapolation unless absolutely necessary.
c) Visual estimates (without a formula) are sufficient if the data do not vary drastically.
- This statement can be somewhat subjective. While visual estimates may work in some cases where data is stable and does not vary much, they can still lead to inaccuracies. Relying solely on visual estimates is not a rigorous approach.
Based on this analysis, the most correct statement is:
b) Extrapolation beyond the table’s highest or lowest temperature can yield large errors and should be avoided unless no other data exist.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Beyond the Answer
Linear interpolation is a neat trick often employed in mathematics and data analysis! It’s precise for the two data points you pick, but it’s important to remember that this method may oversimplify situations where the actual data has a curve or varied behavior in between. Meanwhile, extrapolation can be a bit of a wild card; going beyond your data points is risky and can lead to unreliable predictions, especially if the data has not shown consistent movement.
If you’re working with data that’s somewhat stable, relying on your intuition can sometimes work wonders! Visual estimates can give you a quick and handy insight, but be cautious – even small fluctuations can throw off your estimates, so always back them up with solid reasoning or calculations when possible!
