1. **Problem Statement:** We have kilometers-per-liter data for 13 cars tested in city and highway conditions. We need to calculate the mean, median, and mode for both city and highway data and compare their performances. 2. **Formulas and Definitions:** - Mean: $$\text{Mean} = \frac{\sum x_i}{n}$$ where $x_i$ are data points and $n$ is the number of points. - Median: The middle value when data is sorted. - Mode: The most frequently occurring value. 3. **City Data:** 16.2, 16.7, 15.9, 14.4, 13.2, 15.3, 16.8, 16.0, 16.1, 15.3, 15.2, 15.3, 16.2 - Sorted: 13.2, 14.4, 15.2, 15.3, 15.3, 15.3, 15.9, 16.0, 16.1, 16.2, 16.2, 16.7, 16.8 - Mean: $$\frac{16.2 + 16.7 + 15.9 + 14.4 + 13.2 + 15.3 + 16.8 + 16.0 + 16.1 + 15.3 + 15.2 + 15.3 + 16.2}{13} = \frac{202.6}{13} \approx 15.58$$ - Median: 7th value in sorted list = 15.9 - Mode: 15.3 (appears 3 times) 4. **Highway Data:** 19.4, 20.6, 18.3, 18.6, 19.2, 17.4, 17.2, 18.6, 19.0, 21.1, 19.4, 18.5, 18.7 - Sorted: 17.2, 17.4, 18.3, 18.5, 18.6, 18.6, 18.7, 19.0, 19.2, 19.4, 19.4, 20.6, 21.1 - Mean: $$\frac{19.4 + 20.6 + 18.3 + 18.6 + 19.2 + 17.4 + 17.2 + 18.6 + 19.0 + 21.1 + 19.4 + 18.5 + 18.7}{13} = \frac{244}{13} \approx 18.77$$ - Median: 7th value in sorted list = 18.7 - Mode: 18.6 and 19.4 (each appears twice) 5. **Interpretation:** - The highway mean (18.77) is higher than the city mean (15.58), indicating better fuel efficiency on highways. - The median values also show highway (18.7) is higher than city (15.9), confirming the trend. - Modes show city mode is 15.3 while highway modes are 18.6 and 19.4, again indicating better highway performance. 6. **Conclusion:** Cars generally have better kilometers-per-liter performance on highways than in city driving, as shown by higher mean, median, and mode values for highway data.