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16 Sep 2014, 00:45
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Is the standard deviation of set \(S\) greater than the standard deviation of set \(T\)?
(1) The range of set \(S\) is greater than the range of set \(T\)
(2) The mean of set \(S\) is greater than the mean of set \(T\)
(1) The range of set \(S\) is greater than the range of set \(T\)
(2) The mean of set \(S\) is greater than the mean of set \(T\)
16 Sep 2014, 00:45
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Official Solution:
Is the standard deviation of set \(S\) greater than the standard deviation of set \(T\)?
The standard deviation is a measure of the variation of the data points from the mean, a measure of how widespread a given set is. When the standard deviation is low, the data points tend to be close to the mean, while a high standard deviation implies that the data is spread out over a broader range of values.
(1) The range of set \(S\) is greater than the range of set \(T\).
This implies that the largest and smallest numbers in \(S\) are more widespread than the largest and smallest numbers in \(T\). However, what about the other numbers in these sets?
The standard deviation of {0, 10} is greater than the standard deviation of {0, 9}, but the standard deviation of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than the standard deviation of {0, 9}. Not sufficient.
(2) The mean of set \(S\) is greater than the mean of set \(T\).
Information about the mean is not helpful in determining how widespread the given sets are. Not sufficient.
(1)+(2) Statement (2) provides no additional information for (1), so even when taken together, they are still insufficient to answer the question.
Answer: E
Is the standard deviation of set \(S\) greater than the standard deviation of set \(T\)?
The standard deviation is a measure of the variation of the data points from the mean, a measure of how widespread a given set is. When the standard deviation is low, the data points tend to be close to the mean, while a high standard deviation implies that the data is spread out over a broader range of values.
(1) The range of set \(S\) is greater than the range of set \(T\).
This implies that the largest and smallest numbers in \(S\) are more widespread than the largest and smallest numbers in \(T\). However, what about the other numbers in these sets?
The standard deviation of {0, 10} is greater than the standard deviation of {0, 9}, but the standard deviation of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than the standard deviation of {0, 9}. Not sufficient.
(2) The mean of set \(S\) is greater than the mean of set \(T\).
Information about the mean is not helpful in determining how widespread the given sets are. Not sufficient.
(1)+(2) Statement (2) provides no additional information for (1), so even when taken together, they are still insufficient to answer the question.
Answer: E
General Discussion
05 May 2023, 12:43
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
