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 find the mean absolute deviation (MAD) for each dataset, we first need to calculate the absolute deviation of each data point from the mean and then find the average of these absolute deviations.
For Dataset #1:
Mean = 10
Absolute deviations from the mean:
|5-10| = 5
|8-10| = 2
|9-10| = 1
|10-10| = 0
|12-10| = 2
|12-10| = 2
|14-10| = 4
Average absolute deviation = (5 + 2 + 1 + 0 + 2 + 2 + 4) / 7 = 16 / 7 ≈ 2.29
For Dataset #2:
Mean = 10
Absolute deviations from the mean:
|5-10| = 5
|6-10| = 4
|8-10| = 2
|9-10| = 1
|10-10| = 0
|10-10| = 0
|22-10| = 12
Average absolute deviation = (5 + 4 + 2 + 1 + 0 + 0 + 12) / 7 = 24 / 7 ≈ 3.43
Since Dataset #2 has a larger mean absolute deviation (3.43) compared to Dataset #1 (2.29), Dataset #2 is more spread out.
finish the sentence
Therefore, Dataset #2 is more spread out than Dataset #1 based on their mean absolute deviations.
complete the sentence
Dataset # ? is more spread out because it has a mean absolute deviation of ? while Dataset # ? has a mean absolute deviation of ?.