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 point)
First, let's calculate the mean absolute deviation for each dataset.
Dataset A:
1. Find the mean of Dataset A:
Mean = (9+9+10+10+10+11+12+14+14+18) / 10 = 118 / 10 = 11.8
2. Calculate the absolute deviation for each data point by subtracting the mean from each value and taking the absolute value:
|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
3. Calculate the average of the absolute deviations:
Average Absolute Deviation = (2.8+2.8+1.8+1.8+1.8+0.8+0.2+2.2+2.2+6.2) / 10 = 22.6 / 10 = 2.26
Dataset B:
1. Find the mean of Dataset B:
Mean = (7+8+8+9+10+10+11+11+12+15) / 10 = 101 / 10 = 10.1
2. Calculate the absolute deviation for each data point by subtracting the mean from each value and taking the absolute value:
|7 - 10.1| = 3.1
|8 - 10.1| = 2.1
|8 - 10.1| = 2.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|11 - 10.1| = 0.9
|11 - 10.1| = 0.9
|12 - 10.1| = 1.9
|15 - 10.1| = 4.9
3. Calculate the average of the absolute deviations:
Average Absolute Deviation = (3.1+2.1+2.1+1.1+0.1+0.1+0.9+0.9+1.9+4.9) / 10 = 17.2 / 10 = 1.72
Now, let's calculate how much the mean absolute deviation of Dataset A exceeds that of Dataset B:
Mean Absolute Deviation of Dataset A - Mean Absolute Deviation of Dataset B = 2.26 - 1.72 = 0.54 (rounded to two decimal places)
Therefore, the mean absolute deviation of Dataset A exceeds that of Dataset B by 0.54.