Set X consists of 8 integers. Is the standard deviation..

[RoiC313]

Set X consists of 8 integers. Is the standard deviation of set X equal to zero?

(1) The range of set X is equal to 3

(2) The mean of set X is equal to 5

Set contains distinct elements.

If it consists of more than one integer, It cannot have zero standard deviation. the data in both (1) and (2) is not necessary..

What am I missing here..?

[jnelson0612]

Set X consists of 8 integers. Is the standard deviation of set X equal to zero?

(1) The range of set X is equal to 3

(2) The mean of set X is equal to 5

Set contains distinct elements.

If it consists of more than one integer, It cannot have zero standard deviation. the data in both (1) and (2) is not necessary..

What am I missing here..?

You appear to understand standard deviation, but for those reading this in the future, standard deviation just indicates the difference between the elements of the set and the mean of the set. The only way to have a standard deviation of zero is to have all members of the set be the same value.

Thus we can rephrase this question as the following: Are the members of set X identical?

Statement 1 tells us that the range of the set is 3. That means that there is a difference of 3 between the largest member and the smallest member. Thus, the members of the set X are NOT identical. Thus, we can answer the rephrased question NO. Remember, NO is a sufficient answer; thus statement 1 is sufficient. Our possible answers at this point are A or D.

Statement 2 tells me that the mean of set X is 5. That does not help. My set could be 5, 5, 5, (identical numbers) or 4, 5, 6 (different numbers). I cannot tell from this if the numbers are identical. Insufficient.

Thus, the answer is A.

Please let us know if you have further questions!

[RoiC313]

You appear to understand standard deviation, but for those reading this in the future, standard deviation just indicates the difference between the elements of the set and the mean of the set. The only way to have a standard deviation of zero is to have all members of the set be the same value...

But how can a set of 8 integers can have all its members of the same value if Set is defined to be a collection of distinct objects?

I think this question is flawed...

[tim]

Please post a screen shot of the question that includes reference to the assertion that a set must contain distinct values. To my knowledge there is no such requirement.

[RoiC313]

en.wikipedia.org/wiki/Set_(mathematics)

I can't find now the question explanation that stated so, but i think i recall one.

Anyway, this is the mathematical definition and i don't remember having this ambiguity in a OG question.

My exam is tomorrow, and i will be happy if you could clarify this issue.

Thanks!

[RonPurewal]

en.wikipedia.org/wiki/Set_(mathematics)

I can't find now the question explanation that stated so, but i think i recall one.

Anyway, this is the mathematical definition and i don't remember having this ambiguity in a OG question.

My exam is tomorrow, and i will be happy if you could clarify this issue.

Thanks!

In the math sense, yes, a "set" has to contain distinct values. And that's why the GMAT will not use that definition.
The GMAT will never contain "tricky" questions that require obscure definitions.
Never.

* They scrupulously avoid writing such questions in the first place. Even semi-obscure facts (e.g., 1 is not prime) are never tested on the exam.

* Even if such a question were to appear, it would not pass the "experimental" phase, as it wouldn't generate the right kind of pattern of responses.

So, not to worry.

What is the original source of this problem?
This is the MGMAT CAT folder. Did you actually see this problem on a MGMAT practice test?

[RoiC313]

Thanks for the detailed answer!

It is from MGMAT CAT - the question is called: "Zero Standard Deviation"

[jnelson0612]

Thanks for the detailed answer!

It is from MGMAT CAT - the question is called: "Zero Standard Deviation"

I googled repeatedly and found other posts about it (in other forums) and none of them mentioned the requirement that the numbers were distinct. The original poster added that in but it's not part of the original question. It really wouldn't make sense to say that for this problem . . . then you can answer the question without either of the statements. You will never see a Data Sufficiency question like that.

[RonPurewal]

The question has been updated so that the text says "list" rather than "set", just in case anyone should happen to approach it from the standpoint of formal terminology.

Thanks.