1. **Problem statement:** We are given two sets of mass measurements for sunflower seed bags: one set for 227g bags and one for 454g bags. The standard deviation for the 227g bags is given as $\sigma=5.2$. We need to find the standard deviation for the 454g bags and then discuss how measures of dispersion help compare accuracy. 2. **Formula for standard deviation:** The standard deviation $\sigma$ measures the spread of data around the mean and is calculated as: $$\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^N (x_i - \mu)^2}$$ where $N$ is the number of data points, $x_i$ are the data values, and $\mu$ is the mean. 3. **Calculate the mean for 454g bags:** Sum the masses: $$458 + 445 + 457 + 458 + 452 + 457 + 445 + 452 + 463 + 455 + 451 + 460 + 455 + 453 + 456 + 459 + 451 + 455 + 456 + 450 = 9103$$ Number of bags $N=20$ Mean: $$\mu = \frac{9103}{20} = 455.15$$ 4. **Calculate variance for 454g bags:** Calculate each squared difference $(x_i - \mu)^2$ and sum: $$(458-455.15)^2 + (445-455.15)^2 + \cdots + (450-455.15)^2 = 588.8$$ 5. **Calculate standard deviation for 454g bags:** $$\sigma = \sqrt{\frac{588.8}{20}} = \sqrt{29.44} \approx 5.43$$ 6. **Interpretation:** The standard deviation for the 454g bags is approximately $5.43$ grams. 7. **Using measures of dispersion to compare accuracy:** Measures of dispersion like standard deviation show how spread out the measurements are around the mean. A smaller standard deviation means measurements are more consistent and thus more accurate. Comparing the standard deviations of the two bag sizes ($5.2$ for 227g bags and $5.43$ for 454g bags) shows that both have similar variability, indicating similar accuracy in measurement. **Final answers:** - Standard deviation for 454g bags: $\boxed{5.43}$ - Measures of dispersion help determine if the accuracy of measurements is similar by comparing how spread out the data are around their means.