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.