1. **Stating the problem:** We have two data sets: midterm scores and travel times. We want to analyze the first data set, the midterm scores. 2. **Formula and rules:** To analyze scores, we can find measures like mean (average), median, mode, and range. - Mean formula: $$\text{Mean} = \frac{\sum \text{scores}}{\text{number of scores}}$$ - Median: the middle value when data is sorted. - Mode: the most frequent value. - Range: difference between max and min values. 3. **Calculate mean:** Sum all midterm scores: $$54 + 41 + 53 + 34 + 38 + 44 + 38 + 26 + 42 + 46 + 44 + 47 + 35 + 40 + 37 + 34 + 36 + 34 + 33 + 38 + 60 + 39 + 38 + 46 + 46 + 56 + 47 + 41 + 36 + 45 + 28 + 57 + 40 + 46 + 54 + 52 + 34 + 41 + 34 + 57 + 54 + 32 = 1563$$ Number of scores = 42 Mean = $$\frac{1563}{42} = 37.21$$ (rounded to two decimals) 4. **Calculate median:** Sort scores and find middle value(s). Sorted scores: 26, 28, 32, 33, 34, 34, 34, 34, 35, 36, 36, 37, 38, 38, 38, 38, 39, 40, 40, 41, 41, 42, 44, 44, 45, 46, 46, 46, 46, 47, 47, 52, 53, 54, 54, 54, 56, 57, 57, 60 Since 42 is even, median is average of 21st and 22nd values: 21st = 41, 22nd = 42 Median = $$\frac{41 + 42}{2} = 41.5$$ 5. **Calculate mode:** The most frequent score is 34 and 38 (each appears 4 times). 6. **Calculate range:** Max score = 60, Min score = 26 Range = $$60 - 26 = 34$$ **Final answers:** - Mean = 37.21 - Median = 41.5 - Mode = 34 and 38 - Range = 34