Question

distinguish between the absolute error and the relative error in a measurement. give an example in which the absolute error is large but the relative error is small and another example in which the absolute error is small but the relative error is large. give an example in which the absolute error is large but the relative error is small. a. a runners true weight is 125 pounds, but a scale says he weighs 130 pounds. b. a chemist has 2.9 mg of substance, but a scale measures 2.1 mg. c. a census says that the population of a town is 72,453, but the true population is 96,000. d. a company projects sales of $7.30 billion and true sales turn out to be $7.32 billion. give an example in which the absolute error is small but the relative error is large. a. a runners true weight is 125 pounds, but a scale says he weighs 130 pounds. b. a chemist has 2.9 mg of substance, but a scale measures 2.1 mg. c. a woman weighs 102.4 pounds. the scale at the gym says she weighs 102.7, but the scale at the doctors

Explanation:

Absolute error is the magnitude of the difference between the measured value and the true value. Relative error is the ratio of the absolute error to the true value. For the first part, we calculate absolute and relative error for each option. For the second part, we do the same.

• Option A (first question):
• Absolute error: \(|130 - 125|=5\)
• Relative error: \(\frac{5}{125}=0.04\)
• Option B (first question):
• Absolute error: \(|2.1 - 2.9| = 0.8\)
• Relative error: \(\frac{0.8}{2.9}\approx0.276\)
• Option C (first question):
• Absolute error: \(|72453 - 96000|=23547\)
• Relative error: \(\frac{23547}{96000}\approx0.245\)
• Option D (first question):
• Absolute error: \(|7.32 - 7.30| = 0.02\)
• Relative error: \(\frac{0.02}{7.30}\approx0.0027\)
• Option A (second question):
• Absolute error: \(|130 - 125|=5\)
• Relative error: \(\frac{5}{125}=0.04\)
• Option B (second question):
• Absolute error: \(|2.1 - 2.9| = 0.8\)
• Relative error: \(\frac{0.8}{2.9}\approx0.276\)
• Option C (second question):
• Absolute error: \(|102.7 - 102.4|=0.3\)
• Relative error: \(\frac{0.3}{102.4}\approx0.0029\)

Answer:

• For the example where absolute error is large but relative error is small: A. A runner’s true weight is 125 pounds, but a scale says he weighs 130 pounds
• For the example where absolute error is small but relative error is large: B. A chemist has 2.9 mg of substance, but a scale measures 2.1 mg