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# Is the standard deviation of set S greater than the standard

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Is the standard deviation of set S greater than the standard [#permalink]

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24 Jul 2010, 16:13
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Question Stats:

62% (00:39) correct 38% (00:42) wrong based on 87 sessions

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Is the standard deviation of set S greater than the standard deviation of set T ?

A) The range of set S is greater than the range of set T
B) The mean of set S is greater than the mean of set T

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
[Reveal] Spoiler: OA

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Re: standard deviation of set S and T [#permalink]

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24 Jul 2010, 16:25
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noboru wrote:
Is the standard deviation of set S greater than the standard deviation of set T ?

A) The range of set S is greater than the range of set T
B) The mean of set S is greater than the mean of set T

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Standard deviation is basically the deviation of the terms from the mean.

Statement 1: No information about the Mean,number of terms hence not sufficient.
Statement 2: No information about the number of terms, hence not sufficient.

Even if we take them together, we cannot calculate the |mean - term| for all the terms. We even do not have number of terms.
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Re: standard deviation of set S and T [#permalink]

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26 Jul 2010, 01:54
Suppose that S is (3,3,3,3,3,3,3,3,3,3,1000)
and T is (50,100,150,200,250,300,350,400,450,500,550)
then the range of S is great than that of T while the standard deviation of S is less than that of T, regardless of their means

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Re: Is the standard deviation of set S greater than the standard [#permalink]

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07 Dec 2015, 10:17
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Re: Is the standard deviation of set S greater than the standard [#permalink]

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26 Dec 2016, 01:39
Excellent Question.
It is testing our knowledge of standard deviation.
Lets use some test cases here ->

Statement 1->
1,2,3
1,1,1

Yes

2,4,...100
1,99,99,99,...99

NO

Hence not sufficient

Statement 2->
2,2,2
1,1,1
NO
2,2,4
1,1,1

YES

Hence not sufficient
Combing the two statements

2,4,6...100
1,1,1..1

YES

2,4,6..100,101
1,99,1,99,1,99,1,99

NO

Hence Not sufficient

Hence E

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Re: Is the standard deviation of set S greater than the standard   [#permalink] 26 Dec 2016, 01:39
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