To find the mean score given the scores and their corresponding frequencies, we will follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understand the Data We have two sets of data: - **Scores**: 4, 7, 8, 11, 13, 8 - **Frequencies**: 3, 5, 2, 7, 2, 1 This means: - The score of 4 occurs 3 times. - The score of 7 occurs 5 times. - The score of 8 occurs 2 times. - The score of 11 occurs 7 times. - The score of 13 occurs 2 times. - The score of 8 occurs again 1 time. ### Step 2: Calculate the Total Score To find the mean, we first need to calculate the total score by multiplying each score by its frequency and then summing these products. **Calculations**: - For score 4: \(4 \times 3 = 12\) - For score 7: \(7 \times 5 = 35\) - For score 8 (first occurrence): \(8 \times 2 = 16\) - For score 11: \(11 \times 7 = 77\) - For score 13: \(13 \times 2 = 26\) - For score 8 (second occurrence): \(8 \times 1 = 8\) Now, we sum these products: \[ \text{Total Score} = 12 + 35 + 16 + 77 + 26 + 8 = 174 \] ### Step 3: Calculate the Total Frequency Next, we need to calculate the total frequency by summing all the frequencies: \[ \text{Total Frequency} = 3 + 5 + 2 + 7 + 2 + 1 = 20 \] ### Step 4: Calculate the Mean The mean is calculated using the formula: \[ \text{Mean} = \frac{\text{Total Score}}{\text{Total Frequency}} \] Substituting the values we calculated: \[ \text{Mean} = \frac{174}{20} = 8.7 \] ### Conclusion Thus, the mean score is **8.7**, which corresponds to option **B**. ### Explanation of Other Options - **Option A (7.0)**: This is incorrect because it underestimates the total score based on the frequencies provided. - **Option C (9.5)**: This option is also incorrect as it suggests a higher mean than what the calculations show. It may arise from miscalculating the total score or frequency. - **Option D (11.0)**: This option is incorrect as it implies a mean that is higher than the highest score weighted by its frequency, which is not possible. ### Revision Summary - The mean is calculated by dividing the total score by the total frequency. - Always multiply each score by its frequency before summing to find the total score. - Ensure to sum all frequencies accurately to avoid errors in the mean calculation. - The correct mean score for the given data is **8.7** (Option B).