Question

A set of measurements of a certain parameter is: $20.00,\; 19.75,\; 18.25,\; 17.01$. Find the relative error for the set of measurements.

• A. $0.12$
• B. $0.06$
• C. $0.09$
• D. $0.17$

Hint:

For numerical problems on errors, always calculate mean first, then mean absolute error, and finally divide by the mean to get relative error.

Answer 1

The Correct Option is B

To find the relative error for a set of measurements, we need to determine the mean (average) value of the measured data and the absolute error. The relative error is then calculated as the ratio of the absolute error to the mean value.

1. First, calculate the mean of the given measurements:

\(\text{Mean} = \frac{20.00 + 19.75 + 18.25 + 17.01}{4}\)

\(\text{Mean} = \frac{75.01}{4} = 18.7525\)

1. Find the absolute error, which is the difference between each measurement and the mean value, then calculate the average of these differences:

\(\text{Absolute Differences}: |20.00 - 18.7525| = 1.2475\)
\(|19.75 - 18.7525| = 0.9975\)
\(|18.25 - 18.7525| = 0.5025\)
\(|17.01 - 18.7525| = 1.7425\)

\(\text{Mean Absolute Error} = \frac{1.2475 + 0.9975 + 0.5025 + 1.7425}{4}\)

\(\text{Mean Absolute Error} = \frac{4.49}{4} = 1.1225\)

1. Now, calculate the relative error:

\(\text{Relative Error} = \frac{1.1225}{18.7525}\)

\(\text{Relative Error} \approx 0.06\)

Therefore, the relative error for the set of measurements is approximately \(0.06\). The correct answer is $0.06$.