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

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Joined: 16 Jul 2009
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Is the standard deviation of set S greater than the standard deviation  [#permalink]

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24 Jul 2010, 15:13
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Question Stats:

68% (01:13) correct 32% (00:46) wrong based on 154 sessions

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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

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

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24 Jul 2010, 15:25
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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: Is the standard deviation of set S greater than the standard deviation  [#permalink]

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26 Jul 2010, 00:54
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 deviation  [#permalink]

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26 Dec 2016, 00:39
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 deviation  [#permalink]

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03 Jul 2018, 03:47
gurpreetsingh wrote:
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.

Hi..

But I thought the standard deviation is directly proportional to the range?

So I chose A

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

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03 Jul 2018, 10:15
zanaik89 wrote:
gurpreetsingh wrote:
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.

Hi..

But I thought the standard deviation is directly proportional to the range?

So I chose A

Hello

May I know from where you came to know that standard deviation is directly proportional to the range?

Look at this set P = {4, 5, 5, 6}. Range of this set is 2 and Std Dev is square root of 0.5.
Now look at another set Q = {4, 4, 6, 6}. Range of this set is also 2 but its Std Dev is 1, so greater than that of set P.

There is some effect of range for sure, but we cannot say that its 'directly proportional'. What matters is that how far the values deviate from the mean.
Re: Is the standard deviation of set S greater than the standard deviation &nbs [#permalink] 03 Jul 2018, 10:15
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