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 you answers to the nearest tenth.
dataset #1 ( 5,8,9,10,12,12,14)
dataset#3 ( 5,6,8,9,10,10,22)
To determine which dataset is more spread out, we can calculate the mean absolute deviation (MAD) for each dataset.
1. Calculate the mean absolute deviation for Dataset #1:
Mean = 10
MAD = (|5-10| + |8-10| + |9-10| + |10-10| + |12-10| + |12-10| + |14-10|) / 7
MAD = (5 + 2 + 1 + 0 + 2 + 2 + 4) / 7
MAD = 16 / 7
MAD ≈ 2.3
2. Calculate the mean absolute deviation for Dataset #3:
Mean = 10
MAD = (|5-10| + |6-10| + |8-10| + |9-10| + |10-10| + |10-10| + |22-10|) / 7
MAD = (5 + 4 + 2 + 1 + 0 + 0 + 12) / 7
MAD = 24 / 7
MAD ≈ 3.4
Since the mean absolute deviation for Dataset #3 is higher than that of Dataset #1, Dataset #3 is more spread out.