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17 Jun 2020, 01:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
60% (01:03) correct
40%
(01:01)
wrong
based on 337
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History
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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
17 Jun 2020, 03:13
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Case 1-
S = {1,11} and T={1,10}
SD of S > SD of T
Case 2-
S = {1,6,11} and T={1,10}
SD of S < SD of T
Both cases satisfy both statements and give different answer.
Insufficient
E
S = {1,11} and T={1,10}
SD of S > SD of T
Case 2-
S = {1,6,11} and T={1,10}
SD of S < SD of T
Both cases satisfy both statements and give different answer.
Insufficient
E
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17 Jun 2020, 03:25
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IMO A,
Statement 1: The range of set S is greater than the range of set T:
The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s = (Maximum – Minimum)/4.
Therefore if the range of Set S is 10 and Range if set T is 5
The approximate Standard deviation of set S = 10/4 = 2.5
Whereas standard deviation of set T = 5/4 = 1.25
Therefore,
Set S Standard Deviation > Set T Standard Deviation
(Sufficient)
Statement 2: The mean of set S is greater than the mean of set T
Case 1: Let say mean of set S is 8 where Set S is (6,7,8,9,10)
And Set T mean is 6 where set T is (2,4,6,8,10)
Using the range method.
Set T range is higher than Set S making standard deviation of set T is higher than Set S.
Set T SD > Set S SD
Case 2: Let say mean of set S is 8 where Set S is (4,6,8,10,12)
And Set T mean is 6 where set T is (4,5,6,7,8)
Using the range method.
Set T range is lower than Set S making standard deviation of set T is lower than Set S.
Set T SD < Set S SD
(Insufficient)
Posted from my mobile device
Statement 1: The range of set S is greater than the range of set T:
The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s = (Maximum – Minimum)/4.
Therefore if the range of Set S is 10 and Range if set T is 5
The approximate Standard deviation of set S = 10/4 = 2.5
Whereas standard deviation of set T = 5/4 = 1.25
Therefore,
Set S Standard Deviation > Set T Standard Deviation
(Sufficient)
Statement 2: The mean of set S is greater than the mean of set T
Case 1: Let say mean of set S is 8 where Set S is (6,7,8,9,10)
And Set T mean is 6 where set T is (2,4,6,8,10)
Using the range method.
Set T range is higher than Set S making standard deviation of set T is higher than Set S.
Set T SD > Set S SD
Case 2: Let say mean of set S is 8 where Set S is (4,6,8,10,12)
And Set T mean is 6 where set T is (4,5,6,7,8)
Using the range method.
Set T range is lower than Set S making standard deviation of set T is lower than Set S.
Set T SD < Set S SD
(Insufficient)
Posted from my mobile device
