To find the mean absolute deviation (MAD) of a dataset, we first need to calculate the mean of the dataset and then find the absolute deviation of each data point from the mean.
For Dataset A:
Mean = (9+9+10+10+10+11+12+14+14+18)/10
Mean = 118/10
Mean = 11.8
Absolute deviations from the mean:
|9-11.8| = 2.8
|9-11.8| = 2.8
|10-11.8| = 1.8
|10-11.8| = 1.8
|10-11.8| = 1.8
|11-11.8| = 0.8
|12-11.8| = 0.2
|14-11.8| = 2.2
|14-11.8| = 2.2
|18-11.8| = 6.2
MAD of Dataset A = (2.8 + 2.8 + 1.8 + 1.8 + 1.8 + 0.8 + 0.2 + 2.2 + 2.2 + 6.2)/10
MAD of Dataset A = 2.45
Now, let's do the same for Dataset B:
For Dataset B:
Mean = (7+8+8+9+10+10+11+11+12+15)/10
Mean = 91/10
Mean = 9.1
Absolute deviations from the mean:
|7-9.1| = 2.1
|8-9.1| = 1.1
|8-9.1| = 1.1
|9-9.1| = 0.1
|10-9.1| = 0.9
|10-9.1| = 0.9
|11-9.1| = 1.9
|11-9.1| = 1.9
|12-9.1| = 2.9
|15-9.1| = 5.9
MAD of Dataset B = (2.1 + 1.1 + 1.1 + 0.1 + 0.9 + 0.9 + 1.9 + 1.9 + 2.9 + 5.9)/10
MAD of Dataset B = 2.0
Therefore, the mean absolute deviation of Dataset A exceeds that of Dataset B by 0.45 rounded to two decimal places.
By how much does the mean absolute deviation of Dataset A exceed that of Dataset B? Round your answer to two decimal places.
Dataset A: {9, 9, 10, 10, 10, 11, 12, 14, 14, 18}
Dataset B: {7, 8, 8, 9, 10, 10, 11, 11, 12, 15}
1 answer
3 answers