1. **Problem Statement:** We have test scores of 40 students and need to find the mean, median, and mode. 2. **Mean Formula:** The mean is the average of all data points. $$\text{Mean} = \frac{\sum \text{scores}}{\text{number of scores}}$$ 3. **Median Definition:** The median is the middle value when data is ordered. For an even number of data points, it is the average of the two middle values. 4. **Mode Definition:** The mode is the value(s) that appear most frequently. 5. **Step 1: Order the data (already ordered):** 42, 47, 49, 51, 53, 55, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 92, 94, 96, 98 6. **Step 2: Calculate the mean:** $$\sum \text{scores} = 42 + 47 + 49 + 51 + 53 + 55 + 58 + 59 + 60 + 62 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 87 + 88 + 89 + 90 + 92 + 94 + 96 + 98 = 2980$$ $$\text{Mean} = \frac{2980}{40} = 74.5$$ 7. **Step 3: Calculate the median:** Since there are 40 scores (even), median is average of 20th and 21st values. 20th value = 73, 21st value = 74 $$\text{Median} = \frac{73 + 74}{2} = 73.5$$ 8. **Step 4: Find the mode:** All values appear once, so there is no mode (no repeated scores). **Final answers:** - Mean = 74.5 - Median = 73.5 - Mode = None (no repeated scores)