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

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VP
Joined: 30 Jun 2008
Posts: 1018
Is the standard deviation of set S greater than the standard [#permalink]

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01 Nov 2008, 08:52
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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

--== Message from GMAT Club Team ==--

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Current Student
Joined: 28 Dec 2004
Posts: 3310
Location: New York City
Schools: Wharton'11 HBS'12
Re: DS : Standard Deviation [#permalink]

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01 Nov 2008, 09:01
i think its A..

range means smallest value and largest value are further apart in S..so based on that alone SD is going to be higher..
Manager
Joined: 09 Jul 2008
Posts: 109
Location: Dallas, TX
Schools: McCombs 2011
Re: DS : Standard Deviation [#permalink]

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01 Nov 2008, 09:06
Agree with A. Bigger range = data points farther apart, means higher SD.

2 --> Insuff. Bigger mean does not lead to bigger SD
Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown
Re: DS : Standard Deviation [#permalink]

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01 Nov 2008, 09:11
E

stmt1:
{2,4,6,8,10,12} - SD =2,Range-10
{1,3,5,7,9} - SD =2, Range-8

{1,4,7,10} - SD =3,Range-9
{1,3,5,7,9} - SD =2, Range-8
InSuff

stmt2:
{2,4,6,8,10,12} - SD =2, Mean is 7
{1,3,5,7,9,11} - SD =2, Mean is 6

{2,6,10,14,18} - SD =4, Mean is 10
{1,3,5,7,9,11} - SD =2, Mean is 6
InSuff

Together:
{2,6,10,14,18} - SD =4, Mean is 8, Range is 16
{1,3,5,7,9,11} - SD =2, Mean is 6, Range is 10

{2,4,6,8,10,12,14} - SD =2, Mean is 8, Range is 12
{1,3,5,7,9} - SD =2, Mean is 5, Range is 8
InSuff

I definitely won't be solving this problem in such detail, but thought would put different examples together
VP
Joined: 30 Jun 2008
Posts: 1018
Re: DS : Standard Deviation [#permalink]

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01 Nov 2008, 09:52
OA is E
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Manager
Joined: 09 Jul 2008
Posts: 109
Location: Dallas, TX
Schools: McCombs 2011
Re: DS : Standard Deviation [#permalink]

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01 Nov 2008, 11:49
Just when I thought I had figured out SD problems.
Guys, Can you help me to understand this conceptually.

Range only depends on two points. Is that the reason we cannot use the range to estimate an SD?
What information would have helped to answer this DS question?
SVP
Joined: 29 Aug 2007
Posts: 2452
Re: DS : Standard Deviation [#permalink]

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01 Nov 2008, 13:15
amitdgr wrote:
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: Small range with equal number of elements in the sets tells us that the set with smaller range is smaller SD and vice versa but ranges without the number of elements in sets do not tell us which set has larger SD and vice versa.

2: Means alone donot tell us anything about SDs.

Togather: NSF.

Set S: 10, 14, 15, 15, 15, 15, 15, 15, 15, and 21
Range = 11
Mean = 15
SD = 2.624669291 (using excel sheet - just for demonestrating purpose)

Set T: 5 and 15
Range = 10
Mean = 10
SD = 7.071067812 (using excel sheet - just for demonestrating purpose)

Therefore E.
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SVP
Joined: 17 Jun 2008
Posts: 1502
Re: DS : Standard Deviation [#permalink]

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01 Nov 2008, 13:33
kman wrote:
Just when I thought I had figured out SD problems.
Guys, Can you help me to understand this conceptually.

Range only depends on two points. Is that the reason we cannot use the range to estimate an SD?
What information would have helped to answer this DS question?

You are right. Range is only the difference between the highest and lowest value in the set. However, standard deviation is the distance from the mean (remember normal distribution curve).

Another important aspect is to know that standard deviation is relative to the mean. What this means is that even if the absolute mean is higher, standard deviation can be smaller.

With these, it is clear that answer should be E.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: DS : Standard Deviation   [#permalink] 01 Nov 2008, 13:33
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