Question
The mean of each dataset that follows is 62. Which dataset is less spread out? Justify your answer using the mean absolute deviation of each dataset. Round your answers to the nearest tenth.
Dataset #1: {51, 53, 56, 60, 72, 80}
Dataset #2: {49, 55, 61, 63, 70, 74}
(1 point)
Dataset #1 and Dataset #2 are equally spread because they both have a mean absolute deviation of 0.
Dataset #2 is less spread out because it has a mean absolute deviation of 7 whereas Dataset #1 has a mean absolute deviation of approximately 9.3.
Dataset #1 is less spread out because it has a mean absolute deviation of 9.3 whereas Dataset #2 has a mean absolute deviation of 7.
Dataset #1 and Dataset #2 are equally spread because they both have a mean of 62.
Dataset #1: {51, 53, 56, 60, 72, 80}
Dataset #2: {49, 55, 61, 63, 70, 74}
(1 point)
Dataset #1 and Dataset #2 are equally spread because they both have a mean absolute deviation of 0.
Dataset #2 is less spread out because it has a mean absolute deviation of 7 whereas Dataset #1 has a mean absolute deviation of approximately 9.3.
Dataset #1 is less spread out because it has a mean absolute deviation of 9.3 whereas Dataset #2 has a mean absolute deviation of 7.
Dataset #1 and Dataset #2 are equally spread because they both have a mean of 62.
Answers
GPT-4o mini
To find out which dataset is less spread out, we need to calculate the mean absolute deviation (MAD) for both datasets.
**Dataset #1: {51, 53, 56, 60, 72, 80}**
1. Calculate the absolute deviations from the mean (62):
- |51 - 62| = 11
- |53 - 62| = 9
- |56 - 62| = 6
- |60 - 62| = 2
- |72 - 62| = 10
- |80 - 62| = 18
2. Sum of the absolute deviations:
- 11 + 9 + 6 + 2 + 10 + 18 = 56
3. Calculate the mean absolute deviation:
- \( \text{MAD for Dataset #1} = \frac{56}{6} \approx 9.3 \)
**Dataset #2: {49, 55, 61, 63, 70, 74}**
1. Calculate the absolute deviations from the mean (62):
- |49 - 62| = 13
- |55 - 62| = 7
- |61 - 62| = 1
- |63 - 62| = 1
- |70 - 62| = 8
- |74 - 62| = 12
2. Sum of the absolute deviations:
- 13 + 7 + 1 + 1 + 8 + 12 = 42
3. Calculate the mean absolute deviation:
- \( \text{MAD for Dataset #2} = \frac{42}{6} = 7 \)
Now that we have both mean absolute deviations:
- Dataset #1 has a MAD of approximately 9.3.
- Dataset #2 has a MAD of 7.
Since a smaller mean absolute deviation indicates that the dataset is less spread out, we can conclude:
**Dataset #2 is less spread out because it has a mean absolute deviation of 7 whereas Dataset #1 has a mean absolute deviation of approximately 9.3.**
Thus, the correct choice is:
**Dataset #2 is less spread out because it has a mean absolute deviation of 7 whereas Dataset #1 has a mean absolute deviation of approximately 9.3.**
**Dataset #1: {51, 53, 56, 60, 72, 80}**
1. Calculate the absolute deviations from the mean (62):
- |51 - 62| = 11
- |53 - 62| = 9
- |56 - 62| = 6
- |60 - 62| = 2
- |72 - 62| = 10
- |80 - 62| = 18
2. Sum of the absolute deviations:
- 11 + 9 + 6 + 2 + 10 + 18 = 56
3. Calculate the mean absolute deviation:
- \( \text{MAD for Dataset #1} = \frac{56}{6} \approx 9.3 \)
**Dataset #2: {49, 55, 61, 63, 70, 74}**
1. Calculate the absolute deviations from the mean (62):
- |49 - 62| = 13
- |55 - 62| = 7
- |61 - 62| = 1
- |63 - 62| = 1
- |70 - 62| = 8
- |74 - 62| = 12
2. Sum of the absolute deviations:
- 13 + 7 + 1 + 1 + 8 + 12 = 42
3. Calculate the mean absolute deviation:
- \( \text{MAD for Dataset #2} = \frac{42}{6} = 7 \)
Now that we have both mean absolute deviations:
- Dataset #1 has a MAD of approximately 9.3.
- Dataset #2 has a MAD of 7.
Since a smaller mean absolute deviation indicates that the dataset is less spread out, we can conclude:
**Dataset #2 is less spread out because it has a mean absolute deviation of 7 whereas Dataset #1 has a mean absolute deviation of approximately 9.3.**
Thus, the correct choice is:
**Dataset #2 is less spread out because it has a mean absolute deviation of 7 whereas Dataset #1 has a mean absolute deviation of approximately 9.3.**