To find the mean absolute deviation for each data set, we first need to find the mean of each set.
Data Set #1:
Mean = (5 + 8 + 9 + 10 + 12 + 12 + 14) / 7
Mean = 70 / 7
Mean = 10
Next, we calculate the absolute deviation for each value in the set:
|5 - 10| = 5
|8 - 10| = 2
|9 - 10| = 1
|10 - 10| = 0
|12 - 10| = 2
|12 - 10| = 2
|14 - 10| = 4
Then, we calculate the mean absolute deviation for Data Set #1:
(5 + 2 + 1 + 0 + 2 + 2 + 4) / 7
16 / 7
≈ 2.3
Data Set #2:
Mean = (5 + 6 + 8 + 9 + 10 + 10 + 22) / 7
Mean = 70 / 7
Mean = 10
Absolute deviations for each value:
|5 - 10| = 5
|6 - 10| = 4
|8 - 10| = 2
|9 - 10| = 1
|10 - 10| = 0
|10 - 10| = 0
|22 - 10| = 12
Mean absolute deviation for Data Set #2:
(5 + 4 + 2 + 1 + 0 + 0 + 12) / 7
24 / 7
≈ 3.4
Therefore, Data Set #2 is more spread out.