Two volleyball teams, played five matches each. The number points that scored as shown below

Question

Match 1 Team A 18. Team B 29
Match 2 team A 22. Team B 30
Match 3 team A 35. Team B 31
Match 4 team A 25. Team B 30
Match 5 team A 40 Team B 32
Which team has the greater MAD, and what does this tell you
Team B their scores are more spread out
Team A their scores are more consistent
Both teams have the same MAD
Team A their scores are more spread out

Answer 1

To determine which team has a greater Mean Absolute Deviation (MAD), we first need to calculate the mean score for each team and then find the absolute deviation from the mean for each match.

Team A Scores:

1. Match 1: 18
2. Match 2: 22
3. Match 3: 35
4. Match 4: 25
5. Match 5: 40

Mean for Team A: \[ \text{Mean}_A = \frac{18 + 22 + 35 + 25 + 40}{5} = \frac{140}{5} = 28 \]

Absolute Deviations for Team A:

1. |18 - 28| = 10
2. |22 - 28| = 6
3. |35 - 28| = 7
4. |25 - 28| = 3
5. |40 - 28| = 12

Sum of Absolute Deviations for Team A: \[ 10 + 6 + 7 + 3 + 12 = 38 \]

MAD for Team A: \[ \text{MAD}_A = \frac{38}{5} = 7.6 \]

Team B Scores:

1. Match 1: 29
2. Match 2: 30
3. Match 3: 31
4. Match 4: 30
5. Match 5: 32

Mean for Team B: \[ \text{Mean}_B = \frac{29 + 30 + 31 + 30 + 32}{5} = \frac{152}{5} = 30.4 \]

Absolute Deviations for Team B:

1. |29 - 30.4| = 1.4
2. |30 - 30.4| = 0.4
3. |31 - 30.4| = 0.6
4. |30 - 30.4| = 0.4
5. |32 - 30.4| = 1.6

Sum of Absolute Deviations for Team B: \[ 1.4 + 0.4 + 0.6 + 0.4 + 1.6 = 4.4 \]

MAD for Team B: \[ \text{MAD}_B = \frac{4.4}{5} = 0.88 \]

Conclusion:

• Team A MAD: 7.6
• Team B MAD: 0.88

Since Team A has a greater MAD than Team B, it indicates that Team A's scores are more spread out compared to Team B's scores, which are more consistent.

The correct interpretation is: Team A their scores are more spread out.