1. **Stating the problem:** We are given a standard deviation $\sigma = 10$, a variable $x$, the mean $\bar{x}$, and the number of repeated measurements. We want to understand the advantage of reporting the average of several measurements rather than a single measurement. 2. **Key concepts:** - The **standard deviation** $\sigma$ measures the spread or uncertainty in measurements. - The **mean** $\bar{x}$ is the average of repeated measurements. - Repeating measurements reduces random errors and improves accuracy. 3. **Formula for the standard error of the mean:** $$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$ where $n$ is the number of repeated measurements. 4. **Explanation:** - Taking multiple measurements and averaging them reduces the uncertainty by a factor of $\sqrt{n}$. - This means the average is more precise and likely closer to the true value. - Systematic errors (like calibration errors) are not eliminated by averaging, but random errors are reduced. 5. **Answer to the question:** - The correct advantage is: **The average of several measurements is more likely to be closer to the true result than a single measurement is.** This is because averaging reduces random errors and improves the reliability of the result.