Find the absolute and relative errors in the following situations. 43. Your true height is 1.73 meters (5 feet 8 inches), but a nurse in your doctor’s office measures your height as 1.76 meters.
The Correct Answer and Explanation is:
To find the absolute error and relative error in the measurement of your height, we can use the following formulas:
- Absolute Error:
The absolute error is the difference between the measured value and the true value, ignoring the sign (i.e., how far off the measurement is from the truth). Absolute Error=∣Measured Value−True Value∣\text{Absolute Error} = |\text{Measured Value} – \text{True Value}|Absolute Error=∣Measured Value−True Value∣ - Relative Error:
The relative error is the absolute error divided by the true value. It is usually expressed as a percentage to indicate the magnitude of the error relative to the true value. Relative Error=Absolute ErrorTrue Value×100\text{Relative Error} = \frac{\text{Absolute Error}}{\text{True Value}} \times 100Relative Error=True ValueAbsolute Error×100
Given:
- True Height = 1.73 meters
- Measured Height = 1.76 meters
1. Calculate Absolute Error:
The absolute error is:Absolute Error=∣1.76−1.73∣=∣0.03∣=0.03 meters\text{Absolute Error} = |1.76 – 1.73| = |0.03| = 0.03 \, \text{meters}Absolute Error=∣1.76−1.73∣=∣0.03∣=0.03meters
So, the absolute error is 0.03 meters.
2. Calculate Relative Error:
Now, we calculate the relative error:Relative Error=0.031.73×100=1.73%\text{Relative Error} = \frac{0.03}{1.73} \times 100 = 1.73\%Relative Error=1.730.03×100=1.73%
So, the relative error is 1.73%.
Conclusion:
- Absolute Error = 0.03 meters
- Relative Error = 1.73%
This means that the nurse’s measurement was 0.03 meters (or 3 cm) greater than your true height, and the error is 1.73% of your actual height. This relative error provides a sense of how significant the measurement error is in relation to your actual height.
