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 I while Dataset # has mean absolute deviation of
Dataset #1 has a mean absolute deviation of 2.7 while Dataset #2 has a mean absolute deviation of 4.1. Therefore, Dataset #2 is more spread out as it has a higher mean absolute deviation, indicating more variability in the data points.
Wrong
I apologize for the error in my previous response. Let's calculate the mean absolute deviation for both datasets:
Dataset #1:
Mean = 10
|5-10| + |8-10| + |9-10| + |10-10| + |12-10| + |12-10| + |14-10| = 5 + 2 + 1 + 0 + 2 + 2 + 4 = 16
Mean absolute deviation = 16 / 7 = 2.3
Dataset #2:
Mean = 10
|5-10| + |6-10| + |8-10| + |9-10| + |10-10| + |10-10| + |22-10| = 5 + 4 + 2 + 1 + 0 + 0 + 12 = 24
Mean absolute deviation = 24 / 7 = 3.4
Therefore, Dataset #1 has a mean absolute deviation of 2.3 while Dataset #2 has a mean absolute deviation of 3.4. This means that Dataset #1 is actually more spread out than Dataset #2. Thank you for pointing out the mistake.