1. **Problem Statement:** Calculate the mean, median, and mode of the marks obtained by 15 students: 45, 52, 60, 48, 55, 62, 52, 50, 48, 45, 58, 62, 60, 55, 50. 2. **Mean:** The mean is the average of all data points. The formula is: $$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$$ 3. Calculate the sum: $$45 + 52 + 60 + 48 + 55 + 62 + 52 + 50 + 48 + 45 + 58 + 62 + 60 + 55 + 50 = 802$$ 4. Number of values = 15. 5. Calculate the mean: $$\text{Mean} = \frac{802}{15} = 53.47$$ (rounded to two decimal places). 6. **Median:** The median is the middle value when data is arranged in ascending order. 7. Arrange the data: $$45, 45, 48, 48, 50, 50, 52, 52, 55, 55, 58, 60, 60, 62, 62$$ 8. Since there are 15 values (odd number), the median is the 8th value: $$\text{Median} = 52$$ 9. **Mode:** The mode is the value(s) that appear most frequently. 10. Frequency count: - 45 appears 2 times - 48 appears 2 times - 50 appears 2 times - 52 appears 2 times - 55 appears 2 times - 58 appears 1 time - 60 appears 2 times - 62 appears 2 times 11. Multiple values appear twice, so the dataset is multimodal with modes: $$45, 48, 50, 52, 55, 60, 62$$ **Final answers:** - Mean = 53.47 - Median = 52 - Mode = 45, 48, 50, 52, 55, 60, 62