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.
tricky ds SD question
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- vinay1983
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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.
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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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
- vinay1983
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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?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
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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Yes, that's correct.vinay1983 wrote:So is this general conclusion that "If the range is Zero, then the SD is not positive?
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
- ani781
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Hi Brent,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.
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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The range = (largest value in set) - (smallest value in set)ani781 wrote:Hi Brent,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.
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...
So, in the set {-12, -6, 6, 12}, the range = 12 - (-12) = 24
Cheers,
Brent