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tricky ds SD question

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Source: — Data Sufficiency |
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by vinay1983 » Fri Aug 30, 2013 5:28 am
Hmmm certain even numbers= -6,-12,-18-24,6,12,18,24,36,42....
Is SD positive?

Statement 1

Elements are positive
Then 6,12,18,24,30,36

But we don't know how many elements to calculate SD?

Not sufficient

Statement 2

Range is 0

Difference between largest number and smallest number =0

Only possible when both values are same?

then 24-24 or 12-12, no idea

So Not sufficient

Combine

no possible combination exists.

Hence E.
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by Brent@GMATPrepNow » Fri Aug 30, 2013 6:00 am
rishianand7 wrote:Set T consists of a certain number of even integers divisible by 3. Is standard deviation of set T positive?

(1) All elements of set T are positive.
(2) The range of set T is 0

Target question: Is standard deviation of set T positive?

IMPORTANT: The standard deviation of any set is always greater than or equal to zero. So, either the standard deviation is zero or it's positive. The standard deviation will EQUAL ZERO if all of the numbers in the set are IDENTICAL. The standard deviation will BE POSITIVE if the numbers in the set are NOT IDENTICAL.

Statement 1: All elements of set T are positive
There are various sets of numbers that meet this condition. Here are two:
Case a: the numbers are {6, 12, 18}. Since the numbers are not all identical, the standard deviation is positive
Case b: the numbers are {6, 6, 6}. Since the numbers are identical, the standard deviation is zero. In other words, the standard deviation is not positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The range of set T is 0
If the range = 0, then the numbers (or number) in the set are IDENTICAL, which means the standard deviation is zero.
In other words, the standard deviation is definitely not positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by vinay1983 » Fri Aug 30, 2013 6:54 am
Brent@GMATPrepNow wrote:
rishianand7 wrote:Set T consists of a certain number of even integers divisible by 3. Is standard deviation of set T positive?

(1) All elements of set T are positive.
(2) The range of set T is 0

Target question: Is standard deviation of set T positive?

IMPORTANT: The standard deviation of any set is always greater than or equal to zero. So, either the standard deviation is zero or it's positive. The standard deviation will EQUAL ZERO if all of the numbers in the set are IDENTICAL. The standard deviation will BE POSITIVE if the numbers in the set are NOT IDENTICAL.

Statement 1: All elements of set T are positive
There are various sets of numbers that meet this condition. Here are two:
Case a: the numbers are {6, 12, 18}. Since the numbers are not all identical, the standard deviation is positive
Case b: the numbers are {6, 6, 6}. Since the numbers are identical, the standard deviation is zero. In other words, the standard deviation is not positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The range of set T is 0
If the range = 0, then the numbers (or number) in the set are IDENTICAL, which means the standard deviation is zero.
In other words, the standard deviation is definitely not positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Thank you Brent. I know where I am wrong!So is this general conclusion that "If the range is Zero, then the SD is not positive?
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by Brent@GMATPrepNow » Fri Aug 30, 2013 7:04 am
vinay1983 wrote:So is this general conclusion that "If the range is Zero, then the SD is not positive?
Yes, that's correct.

We can be even more specific and say, if the range of a set of numbers is zero, then the standard deviation of that set equals zero.

Cheers,
Brent
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by ani781 » Sun Sep 01, 2013 9:23 am
Statement 2: The range of set T is 0
If the range = 0, then the numbers (or number) in the set are IDENTICAL, which means the standard deviation is zero.
Hi Brent,
Is it not possible that the set consists of numbers like {-12,-6,+12,+6} to give a range of 0 ?
Would not the SD in that case be non zero ?


Thanks in advance...
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by Brent@GMATPrepNow » Sun Sep 01, 2013 9:42 am
ani781 wrote:
Statement 2: The range of set T is 0
If the range = 0, then the numbers (or number) in the set are IDENTICAL, which means the standard deviation is zero.
Hi Brent,
Is it not possible that the set consists of numbers like {-12,-6,+12,+6} to give a range of 0 ?
Would not the SD in that case be non zero ?


Thanks in advance...
The range = (largest value in set) - (smallest value in set)
So, in the set {-12, -6, 6, 12}, the range = 12 - (-12) = 24

Cheers,
Brent
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