The mean of each dataset that follows is 10. Which dataset is more spread out? Justify your answer using the mean absolute deviation of each dataset. Round your answers to the nearest tenth.
Dataset #1: {5,8,9,10,12,12,14}
Dataset #2: {5,6,8,9,10,10,22}
(2 points)
Dataset #
is more spread out because it has a mean absolute deviation of
while Dataset #
has a mean absolute deviation of
.
To calculate the mean absolute deviation for each dataset, we first need to find the absolute deviations of each data point from the mean and then find the average of those absolute deviations.
For Dataset #1:
Absolute deviations: |5-10| = 5, |8-10| = 2, |9-10| = 1, |10-10| = 0, |12-10| = 2, |12-10| = 2, |14-10| = 4
Mean absolute deviation = (5+2+1+0+2+2+4)/7 = 16/7 ≈ 2.3
For Dataset #2:
Absolute deviations: |5-10| = 5, |6-10| = 4, |8-10| = 2, |9-10| = 1, |10-10| = 0, |10-10| = 0, |22-10| = 12
Mean absolute deviation = (5+4+2+1+0+0+12)/7 = 24/7 ≈ 3.4
Therefore, Dataset #1 is more spread out as it has a lower mean absolute deviation compared to Dataset #2.
what's the mean of absolute for both
For Dataset #1:
Mean absolute deviation = (5+2+1+0+2+2+4)/7 = 16/7 ≈ 2.3
For Dataset #2:
Mean absolute deviation = (5+4+2+1+0+0+12)/7 = 24/7 ≈ 3.4