Exam-style question
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Two measurements have the following errors: measurement A has an actual value of 0.5 and a stored value of 0.49; measurement B has an actual value of 500 and a stored value of 499. Calculate the absolute and relative errors for both measurements. Explain which measurement has the greater relative error and why absolute error alone does not show this difference.
Model answer
What a good answer should say
- For measurement A, the absolute error is |0.5 - 0.49| = 0.01 and the relative error is 0.01 / 0.5 = 0.02, or 2%.
- For measurement B, the absolute error is |500 - 499| = 1 and the relative error is 1 / 500 = 0.002, or 0.2%.
- Measurement A has the greater relative error because its error is a larger fraction of the actual value.
- Absolute error values cannot be compared in isolation when the measurements have different magnitudes.
Explanation
Why this works
Absolute error gives the size of the difference in the original units. Relative error puts that difference into proportion by dividing by the actual value.
A smaller absolute error can therefore represent a larger relative error when the original value is small.
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