Practice Robustness in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The property of a result, algorithm, or model remaining valid or approximately correct even when its assumptions are slightly violated.
Is this answer fragile, or does it survive small errors and changes?
Example 1
easyYou estimate \pi \approx 3.14 instead of 3.14159\ldots in the formula A = \pi r^2 with r = 5 cm. Compute the relative error.
Example 2
mediumShow that the median is more robust than the mean as a measure of centre when outliers are present. Use the data set \{2, 3, 4, 5, 100\}.
Example 3
easyIf an input x = 10 has a measurement error of \pm 1, find the range of f(x) = 2x+3 and assess whether f is robust to this error.
Example 4
mediumProve that the statement 'n^2 > n for all n > 1' is robust to replacing > with \ge: does 'n^2 \ge n for all n \ge 1' still hold?