To calculate the Mean Absolute Deviation (MAD) for both teams, we first need to find the mean (average) of each team's data, then determine the absolute deviations from the mean, and finally compute the average of those absolute deviations.
Step 1: Calculate the mean for each team.
Team A:
- Data: 18, 22, 35, 25, 40
- Mean = (18 + 22 + 35 + 25 + 40) / 5 = 140 / 5 = 28
Team B:
- Data: 29, 30, 31, 30, 32
- Mean = (29 + 30 + 31 + 30 + 32) / 5 = 152 / 5 = 30.4
Step 2: Calculate the absolute deviations from the mean.
Team A:
-
Absolute deviations:
- |18 - 28| = 10
- |22 - 28| = 6
- |35 - 28| = 7
- |25 - 28| = 3
- |40 - 28| = 12
-
MAD for Team A = (10 + 6 + 7 + 3 + 12) / 5 = 38 / 5 = 7.6
Team B:
-
Absolute deviations:
- |29 - 30.4| = 1.4
- |30 - 30.4| = 0.4
- |31 - 30.4| = 0.6
- |30 - 30.4| = 0.4
- |32 - 30.4| = 1.6
-
MAD for Team B = (1.4 + 0.4 + 0.6 + 0.4 + 1.6) / 5 = 4.4 / 5 = 0.88
Step 3: Compare the MAD values.
- MAD for Team A = 7.6
- MAD for Team B = 0.88
Conclusion:
Team A has the greater MAD (7.6 compared to 0.88), which indicates that the data points in Team A are more spread out from the mean compared to the data points in Team B. This means Team A experiences greater variability or dispersion in its numbers compared to Team B.