Question

Dataset A, {7,9,9,12}, and dataset B, {6,8,10,13}, both have a mean of 9.25. Calculate the average deviation from the mean of each dataset.

Answer 1

To calculate the average deviation from the mean for each dataset, we first need to find the deviation of each data point from the mean, then calculate the average of those deviations.

For dataset A:
Mean = 9.25
Deviation from the mean for each data point:
7: 9.25 - 7 = 2.25
9: 9.25 - 9 = 0.25
9: 9.25 - 9 = 0.25
12: 12 - 9.25 = 2.75

Calculate the average of these deviations:
(2.25 + 0.25 + 0.25 + 2.75) / 4 = 5.5 / 4 = 1.375

So, the average deviation from the mean for dataset A is 1.375.

For dataset B:
Mean = 9.25
Deviation from the mean for each data point:
6: 9.25 - 6 = 3.25
8: 9.25 - 8 = 1.25
10: 9.25 - 10 = -0.75
13: 13 - 9.25 = 3.75

Calculate the average of these deviations:
(3.25 + 1.25 + 0.75 + 3.75) / 4 = 9 / 4 = 2.25

So, the average deviation from the mean for dataset B is 2.25.