Answer :
Let's analyze the given statements one by one and determine which ones are true based on the rainfall data:
Rainfall in McKesson (inches):
3.76, 2.45, 3.01, 3.82, 2.32, 3.97, 1.74
Rainfall in Sansome (inches):
3.14, 3.01, 2.36, 2.26, 2.12, 2.71, 1.97
1. Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for McKesson's rainfall is nearly twice that of Sansome's.
- The mean absolute deviation (MAD) for McKesson’s rainfall is 0.72.
- The mean absolute deviation (MAD) for Sansome’s rainfall is 0.38.
The MAD of McKesson is indeed nearly twice that of Sansome's (0.72 is approximately twice 0.38), which makes this statement true. Therefore, it implies that comparing their means directly based on MAD might not be very meaningful due to the larger variability in the rainfall data of McKesson.
True
2. Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for Sansome's rainfall is nearly twice that of McKesson's.
- This statement is incorrect because the MAD for Sansome's rainfall (0.38) is not nearly twice that of McKesson's (0.72).
False
3. The difference of the means of the two cities is 0.5.
- The mean rainfall in McKesson is 3.01 inches.
- The mean rainfall in Sansome is 2.51 inches.
- The difference between the means is [tex]\(3.01 - 2.51 = 0.50\)[/tex].
Thus, the difference of the means is indeed 0.5.
True
4. The difference of the means of the two cities is 1.
- As calculated above, the difference in means is 0.50, not 1.
False
Based on the analysis:
- Statement 1 is correct.
- Statement 2 is incorrect.
- Statement 3 is correct.
- Statement 4 is incorrect.
Thus, the correct statements are:
- Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for McKesson's rainfall is nearly twice that of Sansome's.
- The difference of the means of the two cities is 0.5.
Rainfall in McKesson (inches):
3.76, 2.45, 3.01, 3.82, 2.32, 3.97, 1.74
Rainfall in Sansome (inches):
3.14, 3.01, 2.36, 2.26, 2.12, 2.71, 1.97
1. Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for McKesson's rainfall is nearly twice that of Sansome's.
- The mean absolute deviation (MAD) for McKesson’s rainfall is 0.72.
- The mean absolute deviation (MAD) for Sansome’s rainfall is 0.38.
The MAD of McKesson is indeed nearly twice that of Sansome's (0.72 is approximately twice 0.38), which makes this statement true. Therefore, it implies that comparing their means directly based on MAD might not be very meaningful due to the larger variability in the rainfall data of McKesson.
True
2. Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for Sansome's rainfall is nearly twice that of McKesson's.
- This statement is incorrect because the MAD for Sansome's rainfall (0.38) is not nearly twice that of McKesson's (0.72).
False
3. The difference of the means of the two cities is 0.5.
- The mean rainfall in McKesson is 3.01 inches.
- The mean rainfall in Sansome is 2.51 inches.
- The difference between the means is [tex]\(3.01 - 2.51 = 0.50\)[/tex].
Thus, the difference of the means is indeed 0.5.
True
4. The difference of the means of the two cities is 1.
- As calculated above, the difference in means is 0.50, not 1.
False
Based on the analysis:
- Statement 1 is correct.
- Statement 2 is incorrect.
- Statement 3 is correct.
- Statement 4 is incorrect.
Thus, the correct statements are:
- Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for McKesson's rainfall is nearly twice that of Sansome's.
- The difference of the means of the two cities is 0.5.
