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 #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 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 485.6 whereas Dataset #1 has a mean absolute deviation of only 48.2.
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 #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: 401, 467, 489, 503, 568
(1 point)
Responses
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 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 485.6 whereas Dataset #1 has a mean absolute deviation of only 48.2.
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 #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.
Answers
GPT-4o mini
To determine which dataset is more spread out, we compare their mean absolute deviations (MAD).
You stated that the mean absolute deviation of Dataset #1 is 48.2. For Dataset #2, we would need to calculate the mean absolute deviation based on its values (401, 467, 489, 503, 568).
Let's calculate the mean of Dataset #2:
1. Calculate the mean:
\[
\text{Mean} = \frac{401 + 467 + 489 + 503 + 568}{5} = \frac{2428}{5} = 485.6
\]
2. Calculate the absolute deviations from the mean:
- |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 (MAD) for Dataset #2:
\[
\text{MAD} = \frac{84.6 + 18.6 + 3.4 + 17.4 + 82.4}{5} = \frac{206.4}{5} = 41.28
\]
Now we compare both datasets:
- Dataset #1: MAD = 48.2
- Dataset #2: MAD = 41.28
Since Dataset #1 has a larger mean absolute deviation (48.2) compared to Dataset #2 (41.28), we conclude that:
**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 stated that the mean absolute deviation of Dataset #1 is 48.2. For Dataset #2, we would need to calculate the mean absolute deviation based on its values (401, 467, 489, 503, 568).
Let's calculate the mean of Dataset #2:
1. Calculate the mean:
\[
\text{Mean} = \frac{401 + 467 + 489 + 503 + 568}{5} = \frac{2428}{5} = 485.6
\]
2. Calculate the absolute deviations from the mean:
- |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 (MAD) for Dataset #2:
\[
\text{MAD} = \frac{84.6 + 18.6 + 3.4 + 17.4 + 82.4}{5} = \frac{206.4}{5} = 41.28
\]
Now we compare both datasets:
- Dataset #1: MAD = 48.2
- Dataset #2: MAD = 41.28
Since Dataset #1 has a larger mean absolute deviation (48.2) compared to Dataset #2 (41.28), we conclude that:
**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.**