1. The problem asks if the mean represents the center of the data set: 8, 8, 11, 11, 8, 9, 7, 7, 7, 7, 7, 7, 10. 2. The mean (average) is calculated by summing all data points and dividing by the number of points. 3. Formula for mean: $$\text{mean} = \frac{\sum x_i}{n}$$ where $x_i$ are data points and $n$ is the number of points. 4. Calculate the sum: $8+8+11+11+8+9+7+7+7+7+7+7+10 = 104$. 5. Count the number of data points: $n=13$. 6. Calculate the mean: $$\text{mean} = \frac{104}{13} = 8$$. 7. The mean is 8, which is a measure of central tendency. 8. To check if the mean represents the center, consider the data distribution: many values cluster around 7 and 8, with some higher values (9, 10, 11). 9. The mean 8 lies near the middle of the data range and reflects the center well in this case. 10. Therefore, the mean does represent the center of this data set.