Bunuel wrote:
Competition Mode Question
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
Solution:Statement One Alone:The range of set S is greater than the range of set T.
Despite knowing the range of set S is greater than the range of set T, we can’t determine whether the standard deviation of set S is greater than the standard deviation of set T. We have no information about the individual data values in either set, nor do we know the number of elements in either set.
Statement Two Alone:
The mean of set S is greater than the mean of set T.
Despite knowing the mean of set S is greater than the mean of set T, we can’t determine whether the standard deviation of set S is greater than the standard deviation of set T. Again, we have insufficient information about the individual data values in either set and the number of elements in either set.
Statements One and Two Together:
Despite knowing both the range and the mean of set S is greater than the corresponding measures of set T, we still can’t determine whether the standard deviation of set S is greater than the standard deviation of set T. Without knowing any data values in either set, it’s impossible to determine which set has a larger standard deviation.
Answer: E