1. The first problem involves understanding the mean and sample standard deviation of calories in a mid-sized hamburger. 2. The mean is given as $493.30$, which represents the average calorie count of the sample. 3. The sample standard deviation is $20.28$, which measures the spread or variability of the calorie counts around the mean. 4. The formula for the sample mean is $$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$ where $x_i$ are the data points and $n$ is the number of data points. 5. The formula for the sample standard deviation is $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ which calculates the average squared deviation from the mean, adjusted by $n-1$ for sample data. 6. For the second problem, the scatter diagrams show points trending upward, indicating a positive association between $x$ and $y$. 7. A positive association means as $x$ increases, $y$ tends to increase as well. 8. This is typically identified by a scatter plot where points slope upwards from left to right. 9. Therefore, the scatter diagrams located in the bottom-left area with upward trending points suggest a positive correlation between $x$ and $y$. Final answers: - Mean calories: $493.30$ - Sample standard deviation: $20.28$ - Scatter diagrams indicate positive association between $x$ and $y$.