Question
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
Item 2
COURSE TOOLS
Dataset #1 {5,8, 9, 10, 12, 12, 14}
Item 3
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
Item 2
COURSE TOOLS
Dataset #1 {5,8, 9, 10, 12, 12, 14}
Item 3
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
Answers
GPT-4o mini
To determine which dataset is more spread out, we will calculate the Mean Absolute Deviation (MAD) for each dataset.
### Step 1: Define Mean Absolute Deviation (MAD)
The Mean Absolute Deviation is calculated using the following steps:
1. Find the mean (which is given as 10 for both datasets).
2. Calculate the absolute deviation from the mean for each data point.
3. Find the average of these absolute deviations.
### Dataset #1: {5, 8, 9, 10, 12, 12, 14}
- 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
- Sum of absolute deviations:
5 + 2 + 1 + 0 + 2 + 2 + 4 = 16
- Mean Absolute Deviation (MAD):
\[
MAD = \frac{16}{7} \approx 2.3
\]
### Dataset #2: {5, 6, 8, 9, 10, 10, 22}
- 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
- Sum of absolute deviations:
5 + 4 + 2 + 1 + 0 + 0 + 12 = 24
- Mean Absolute Deviation (MAD):
\[
MAD = \frac{24}{7} \approx 3.4
\]
### Conclusion
- **Dataset #1** has a mean absolute deviation of approximately **2.3**.
- **Dataset #2** has a mean absolute deviation of approximately **3.4**.
Thus, **Dataset #2 is more spread out** because it has a mean absolute deviation of **3.4**, while Dataset #1 has a mean absolute deviation of **2.3**.
### Step 1: Define Mean Absolute Deviation (MAD)
The Mean Absolute Deviation is calculated using the following steps:
1. Find the mean (which is given as 10 for both datasets).
2. Calculate the absolute deviation from the mean for each data point.
3. Find the average of these absolute deviations.
### Dataset #1: {5, 8, 9, 10, 12, 12, 14}
- 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
- Sum of absolute deviations:
5 + 2 + 1 + 0 + 2 + 2 + 4 = 16
- Mean Absolute Deviation (MAD):
\[
MAD = \frac{16}{7} \approx 2.3
\]
### Dataset #2: {5, 6, 8, 9, 10, 10, 22}
- 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
- Sum of absolute deviations:
5 + 4 + 2 + 1 + 0 + 0 + 12 = 24
- Mean Absolute Deviation (MAD):
\[
MAD = \frac{24}{7} \approx 3.4
\]
### Conclusion
- **Dataset #1** has a mean absolute deviation of approximately **2.3**.
- **Dataset #2** has a mean absolute deviation of approximately **3.4**.
Thus, **Dataset #2 is more spread out** because it has a mean absolute deviation of **3.4**, while Dataset #1 has a mean absolute deviation of **2.3**.