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Set T consists of a certain number of even integers

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Set T consists of a certain number of even integers [#permalink]

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New post 19 Oct 2008, 05:44
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

1:All elements of set T are positive
2:The range of set T is 0

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Re: Standard Deviation [#permalink]

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New post 19 Oct 2008, 07:29
vishalgc wrote:
Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

1:All elements of set T are positive
2:The range of set T is 0


B.

1: T could have diffierent or same +ve integers. nsf...
2: T has same +ve integers. so range = 0. Hence T has zero (0) or non-positive SD. suff.
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Re: Standard Deviation [#permalink]

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New post 19 Oct 2008, 07:49
vishalgc wrote:
Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

1:All elements of set T are positive
2:The range of set T is 0


2)solves the issue since 0 = range means all equal values !!!SD=0 which is neither +ve nor -ve
1)All elements are +ve means the deviation is always +ve irrespective of individual values!!!

IMO D

one doubt is that I thought SD is always +ve since its RMS value of deviations !!!Please clearify and is the AREA of the graph !!
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Re: Standard Deviation [#permalink]

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New post 19 Oct 2008, 11:14
IMO A

still same doubt! Where did you get this que from?

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Re: Standard Deviation [#permalink]

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New post 19 Oct 2008, 11:26
Me too.

I would bet all my money to say that SD is always +ive

SD=sqrt(sum((xi-mean)^2))

How can be it -ive?

What is the source of the problem?

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Re: Standard Deviation [#permalink]

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New post 19 Oct 2008, 16:36
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IMO B

1.) T= (6,12). i.e SD>0
or
T = (6,6,6). i.e, SD = 0
Insuff

2.) all the numbers are same
Therefore, SD = 0
Suff..

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Re: Standard Deviation [#permalink]

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New post 20 Oct 2008, 02:30
This is a wrong question. SD is always positive.
The basic idea of the standard deviation is that you're measuring variations around the mean value. Some of those values will be below the mean, some above and sometimes you'll have some that are equal to the mean. In other words some of the differences between the individual measurements will be positive (more than the mean), some will be negative (below the mean) and some will be zero (directly equal to the mean). Now just adding these differences up is dangerous because the positive and negative values will cancel each other out. For example, to take an incredibly simplistic case, if you've got a sample of two values, one of 9 and one of 11, the mean is equal to 10. The differences are -1 and +1, adding these together gives us a total variation of 0. But we know that there's not zero variation around that mean value!

So, to get round this problem each of the variations around the mean is squared. When you square a negative value you get a positive value.

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Re: Standard Deviation [#permalink]

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New post 20 Oct 2008, 02:52
Calculation of Standard Deviation (SD):
    i) Find the mean of the set of numbers
    ii) Find the difference between each of the numbers and the mean
    iii) Square the differences and take the mean of the differences
    iv) Take the positive square root of this value

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Re: Standard Deviation [#permalink]

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New post 20 Oct 2008, 05:08
rishi2377 wrote:
This is a wrong question. SD is always positive.


SD can be 0, which is not +ve.
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Re: Standard Deviation [#permalink]

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New post 20 Oct 2008, 09:49
GMAT TIGER wrote:
rishi2377 wrote:
This is a wrong question. SD is always positive.


SD can be 0, which is not +ve.


mmm, good point GMAT TIGER. I didn't see it

if I consider the problem again, taking into account that SD can be 0 or greater than 0:

1 Suff. because all elements are greater than 0. The solution is "yes"

2 Suff. because the range equals 0 means that the maximum number and the minimum are equal. Therefore, SD = 0. Answer "no"

However, I get 2 different answers which I think is not possible on a real GMAT exam, isn't it?
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Re: Standard Deviation   [#permalink] 20 Oct 2008, 09:49
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