The mean of the following dataset is 8. Find the mean absolute deviation of the dataset.
{5.8,7,8.1,9.2,9.9} (1 point)
The mean absolute deviation is
.
Find the mean absolute deviation of the following dataset.
{21,25,25,26,26,27,28,30} (1 point)
The mean absolute deviation is
.Tessa is investigating the number of strawberries in a 1-pound package. She has 6 packages of strawberries and counts the number of strawberries in each package. Her results follow.
{10,12,14,15,16,17}
What is the mean absolute deviation of her data?
(1 point)
The mean absolute deviation is
.
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
.
The mean absolute deviation of Dataset #1 is 5.6. The mean absolute deviation of Dataset #2 is 11.8. Which dataset is less spread out?(1 point)
Dataset #
is less spread out.
3 answers
1. Mean absolute deviation of {5.8, 7, 8.1, 9.2, 9.9}:
Mean = (5.8 + 7 + 8.1 + 9.2 + 9.9) / 5 = 40 / 5 = 8
Absolute deviations from the mean: {2.2, 1, 0.1, 1.2, 1.9}
Mean absolute deviation = (2.2 + 1 + 0.1 + 1.2 + 1.9) / 5 = 6.4 / 5 = 1.28
2. Mean absolute deviation of {21, 25, 25, 26, 26, 27, 28, 30}:
Mean = (21 + 25 + 25 + 26 + 26 + 27 + 28 + 30) / 8 = 212 / 8 = 26.5
Absolute deviations from the mean: {4.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1.5, 3.5}
Mean absolute deviation = (4.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 1.5 + 3.5) / 8 = 12.5 / 8 = 1.5625
3. Mean absolute deviation of Tessa's data {10, 12, 14, 15, 16, 17}:
Mean = (10 + 12 + 14 + 15 + 16 + 17) / 6 = 84 / 6 = 14
Absolute deviations from the mean: {4, 2, 0, 1, 2, 3}
Mean absolute deviation = (4 + 2 + 0 + 1 + 2 + 3) / 6 = 12 / 6 = 2
4. Comparing Dataset #1 and Dataset #2:
Dataset #1: Mean absolute deviation = 5.6
Dataset #2: Mean absolute deviation = 11.8
The mean absolute deviation of Dataset #1 (5.6) is smaller than that of Dataset #2 (11.8), indicating that Dataset #1 is less spread out.
Therefore:
1. The mean absolute deviation of {5.8, 7, 8.1, 9.2, 9.9} is 1.28
2. The mean absolute deviation of {21, 25, 25, 26, 26, 27, 28, 30} is 1.5625
3. The mean absolute deviation of Tessa's data {10, 12, 14, 15, 16, 17} is 2
4. Dataset #1 ({5, 8, 9, 10, 12, 12, 14}) is more spread out, while Dataset #2 ({5, 6, 8, 9, 10, 10, 22}) is less spread out.
1 answer