Question

Scores of two teams across sis games team1 { 6, 0, 4, 17, 3, 12} Tram 2. { 23, 14, 22, 14, 17, 22} what is the range of both teams and what team has a more consistent number of goal scored?

Answer 1

To find the range of scores for each team, we need to subtract the minimum score from the maximum score.

**Team 1 Scores:** {6, 0, 4, 17, 3, 12}
- Maximum Score = 17
- Minimum Score = 0
- Range = Maximum - Minimum = 17 - 0 = **17**

**Team 2 Scores:** {23, 14, 22, 14, 17, 22}
- Maximum Score = 23
- Minimum Score = 14
- Range = Maximum - Minimum = 23 - 14 = **9**

Now, we can compare the consistency of the two teams. A common method to measure consistency is to calculate the standard deviation of the scores. A lower standard deviation indicates more consistency.

### Calculating the Standard Deviation

1. **Team 1:**
- Mean = (6 + 0 + 4 + 17 + 3 + 12) / 6 = 42 / 6 = 7
- Variance = [(6-7)² + (0-7)² + (4-7)² + (17-7)² + (3-7)² + (12-7)²] / 6
- Variance = [1 + 49 + 9 + 100 + 16 + 25] / 6 = 200 / 6 ≈ 33.33
- Standard Deviation = √33.33 ≈ 5.77

2. **Team 2:**
- Mean = (23 + 14 + 22 + 14 + 17 + 22) / 6 = 112 / 6 ≈ 18.67
- Variance = [(23-18.67)² + (14-18.67)² + (22-18.67)² + (14-18.67)² + (17-18.67)² + (22-18.67)²] / 6
- Variance = [19.36 + 21.78 + 11.11 + 21.78 + 2.78 + 11.11] / 6
- Variance = [87.92] / 6 ≈ 14.65
- Standard Deviation = √14.65 ≈ 3.83

### Summary of Results
- **Range of Team 1:** 17
- **Range of Team 2:** 9
- **Standard Deviation of Team 1:** ≈ 5.77
- **Standard Deviation of Team 2:** ≈ 3.83

### Conclusion
- Team 2 has a smaller range (9) compared to Team 1 (17), indicating that Team 2 has a more consistent score across the games.
- Additionally, Team 2's standard deviation (≈ 3.83) is lower than that of Team 1 (≈ 5.77), confirming that Team 2 is more consistent in scoring.