Question
The mean absolute deviation of Dataset #1 is 48.2. Dataset #2 follows. Which dataset is more spread out?
Dataset #2: 401, 467, 489, 503, 568
(1 point)
Responses
Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 0.
Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 0.
Dataset #2 is more spread out because it has a mean absolute deviation of 41.28, whereas Dataset #1 has a mean absolute deviation of 48.2.
Dataset #2 is more spread out because it has a mean absolute deviation of 41.28, whereas Dataset #1 has a mean absolute deviation of 48.2.
Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 41.28.
Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 41.28.
Dataset #2 is more spread out because it has a mean absolute deviation of 485.6 whereas Dataset #1 has a mean absolute deviation of only 48.2.
Dataset #2: 401, 467, 489, 503, 568
(1 point)
Responses
Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 0.
Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 0.
Dataset #2 is more spread out because it has a mean absolute deviation of 41.28, whereas Dataset #1 has a mean absolute deviation of 48.2.
Dataset #2 is more spread out because it has a mean absolute deviation of 41.28, whereas Dataset #1 has a mean absolute deviation of 48.2.
Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 41.28.
Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 41.28.
Dataset #2 is more spread out because it has a mean absolute deviation of 485.6 whereas Dataset #1 has a mean absolute deviation of only 48.2.
Answers
GPT-4o mini
To determine which dataset is more spread out, we need to compare the mean absolute deviation (MAD) of both datasets.
You provided that the mean absolute deviation of Dataset #1 is 48.2. To compare it to Dataset #2, we can first calculate the mean absolute deviation (MAD) for Dataset #2.
1. Calculate the mean for Dataset #2:
- \( \text{Mean} = \frac{401 + 467 + 489 + 503 + 568}{5} = \frac{2428}{5} = 485.6 \)
2. Calculate the absolute deviations from the mean for Dataset #2:
- \( |401 - 485.6| = 84.6 \)
- \( |467 - 485.6| = 18.6 \)
- \( |489 - 485.6| = 3.4 \)
- \( |503 - 485.6| = 17.4 \)
- \( |568 - 485.6| = 82.4 \)
3. Calculate the mean absolute deviation:
- \( \text{MAD} = \frac{84.6 + 18.6 + 3.4 + 17.4 + 82.4}{5} = \frac{206.4}{5} = 41.28 \)
Now we can compare the two MAD values:
- Dataset #1: MAD = 48.2
- Dataset #2: MAD = 41.28
Since 48.2 > 41.28, **Dataset #1** is more spread out than **Dataset #2**.
Therefore, the correct response is:
- **Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 41.28.**
You provided that the mean absolute deviation of Dataset #1 is 48.2. To compare it to Dataset #2, we can first calculate the mean absolute deviation (MAD) for Dataset #2.
1. Calculate the mean for Dataset #2:
- \( \text{Mean} = \frac{401 + 467 + 489 + 503 + 568}{5} = \frac{2428}{5} = 485.6 \)
2. Calculate the absolute deviations from the mean for Dataset #2:
- \( |401 - 485.6| = 84.6 \)
- \( |467 - 485.6| = 18.6 \)
- \( |489 - 485.6| = 3.4 \)
- \( |503 - 485.6| = 17.4 \)
- \( |568 - 485.6| = 82.4 \)
3. Calculate the mean absolute deviation:
- \( \text{MAD} = \frac{84.6 + 18.6 + 3.4 + 17.4 + 82.4}{5} = \frac{206.4}{5} = 41.28 \)
Now we can compare the two MAD values:
- Dataset #1: MAD = 48.2
- Dataset #2: MAD = 41.28
Since 48.2 > 41.28, **Dataset #1** is more spread out than **Dataset #2**.
Therefore, the correct response is:
- **Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 41.28.**