To determine which team had the best overall record for the season, we need to compare two statistical measures of center: the mean and the median. Let's analyze both measures step-by-step for each team.
Step-by-Step Solution:
### Jaguars
1. Points in Each Game:
[tex]\[3, 14, 7, 7, 21, 10, 17, 6, 14, 24, 21, 7, 10, 17, 3\][/tex]
2. Mean Calculation:
- Sum of the points: [tex]\(3 + 14 + 7 + 7 + 21 + 10 + 17 + 6 + 14 + 24 + 21 + 7 + 10 + 17 + 3 = 181\)[/tex]
- Number of games: 15
- Mean: [tex]\(\frac{181}{15} \approx 12.1\)[/tex]
3. Median Calculation:
- Sorted points: [tex]\([3, 3, 6, 7, 7, 7, 10, 10, 14, 14, 17, 17, 21, 21, 24]\)[/tex]
- The middle value (8th value in the sorted list): [tex]\(10\)[/tex]
- Median: [tex]\(10\)[/tex]
### Falcons
1. Points in Each Game:
[tex]\[24, 24, 10, 7, 30, 28, 21, 6, 17, 16, 35, 30, 28, 24, 14\][/tex]
2. Mean Calculation:
- Sum of the points: [tex]\(24 + 24 + 10 + 7 + 30 + 28 + 21 + 6 + 17 + 16 + 35 + 30 + 28 + 24 + 14 = 314\)[/tex]
- Number of games: 15
- Mean: [tex]\(\frac{314}{15} \approx 20.9\)[/tex]
3. Median Calculation:
- Sorted points: [tex]\([6, 7, 10, 14, 16, 17, 21, 24, 24, 24, 28, 28, 30, 30, 35]\)[/tex]
- The middle value (8th value in the sorted list): [tex]\(24\)[/tex]
- Median: [tex]\(24\)[/tex]
### Conclusions:
- The Jaguars have a mean value of about 12.1 points per game.
- The Falcons have a mean value of about 20.9 points per game.
- The median value for the Jaguars is 10 points.
- The median value for the Falcons is 24 points.
Given these calculations, we can see that:
- The Falcons have a higher mean value (20.9 points compared to the Jaguars' 12.1 points).
- The Falcons also have a higher median value (24 points compared to the Jaguars' 10 points).
Thus, the best measure of center to compare in this context is the mean, as it gives an overall picture of the average performance across all games. However, the same conclusion can be drawn using the median since the Falcons also outperform the Jaguars in this measure.
Therefore, the correct answer is:
- Falcons; they have a larger mean value of about 20.9 points.
- Falcons; they have a larger median value of 24 points.
