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
1.04
It's not that
My apologies for the mistake. Let's re-calculate the mean absolute deviation correctly.
1. Calculate the mean (average) of the dataset:
(5.8 + 7 + 8.1 + 9.2 + 9.9) / 5 = 40 / 5 = 8
2. Calculate the deviation from the mean for each data point:
|5.8 - 8| = 2.2
|7 - 8| = 1
|8.1 - 8| = 0.1
|9.2 - 8| = 1.2
|9.9 - 8| = 1.9
3. Calculate the mean absolute deviation:
(2.2 + 1 + 0.1 + 1.2 + 1.9) / 5 = 6.4 / 5 = 1.28
Therefore, the mean absolute deviation of the dataset {5.8, 7, 8.1, 9.2, 9.9} is 1.28.
Find the mean absolute deviation of the following dataset.
{21,25,25,26,26,27,28,30} (1 point)
The mean absolute deviation is ____.
1. First, let's calculate the mean of the dataset:
Mean = (21 + 25 + 25 + 26 + 26 + 27 + 28 + 30) / 8
Mean = 208 / 8
Mean = 26
2. Now, calculate the deviation from the mean for each data point:
|21 - 26| = 5
|25 - 26| = 1
|25 - 26| = 1
|26 - 26| = 0
|26 - 26| = 0
|27 - 26| = 1
|28 - 26| = 2
|30 - 26| = 4
3. Calculate the mean absolute deviation:
Mean of absolute deviations = (5 + 1 + 1 + 0 + 0 + 1 + 2 + 4) / 8
Mean of absolute deviations = 14 / 8
Mean of absolute deviations = 1.75
Therefore, the mean absolute deviation of the dataset {21, 25, 25, 26, 26, 27, 28, 30} is 1.75.
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 ____.
1. First, let's calculate the mean of the dataset:
Mean = (10 + 12 + 14 + 15 + 16 + 17) / 6
Mean = 84 / 6
Mean = 14
2. Now, calculate the deviation from the mean for each data point:
|10 - 14| = 4
|12 - 14| = 2
|14 - 14| = 0
|15 - 14| = 1
|16 - 14| = 2
|17 - 14| = 3
3. Calculate the mean absolute deviation:
Mean of absolute deviations = (4 + 2 + 0 + 1 + 2 + 3) / 6
Mean of absolute deviations = 12 / 6
Mean of absolute deviations = 2
Therefore, the mean absolute deviation of Tessa's data {10, 12, 14, 15, 16, 17} is 2.
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 ____.
1. Calculate the mean absolute deviation for Dataset #1:
1.1 Calculate the mean of Dataset #1:
Mean = (5 + 8 + 9 + 10 + 12 + 12 + 14) / 7
Mean = 70 / 7
Mean = 10
1.2 Calculate the deviation from the mean for each data point in Dataset #1:
|5 - 10| = 5
|8 - 10| = 2
|9 - 10| = 1
|10 - 10| = 0
|12 - 10| = 2
|12 - 10| = 2
|14 - 10| = 4
1.3 Calculate the mean absolute deviation for Dataset #1:
Mean of absolute deviations = (5 + 2 + 1 + 0 + 2 + 2 + 4) / 7
Mean of absolute deviations = 16 / 7 ≈ 2.3
2. Calculate the mean absolute deviation for Dataset #2:
2.1 Calculate the mean of Dataset #2:
Mean = (5 + 6 + 8 + 9 + 10 + 10 + 22) / 7
Mean = 70 / 7
Mean = 10
2.2 Calculate the deviation from the mean for each data point in Dataset #2:
|5 - 10| = 5
|6 - 10| = 4
|8 - 10| = 2
|9 - 10| = 1
|10 - 10| = 0
|10 - 10| = 0
|22 - 10| = 12
2.3 Calculate the mean absolute deviation for Dataset #2:
Mean of absolute deviations = (5 + 4 + 2 + 1 + 0 + 0 + 12) / 7
Mean of absolute deviations = 24 / 7 ≈ 3.4
Therefore, Dataset #2 is more spread out because it has a mean absolute deviation of approximately 3.4, while Dataset #1 has a mean absolute deviation of approximately 2.3.
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.