If the standard deviation of Set Y is 4, what are the

Question

If the standard deviation of Set Y is 4, what are the greatest and least values that are within one standard deviation of the mean?

(1) The median of Set Y is 5.

(2) The mean of Set Y is 6.

vad3tha · Accepted Answer

Standard deviation is how spread out the number are from the mean. The question asked for the greatest and least values that are within one standard deviation of the mean, reading from the question only, we know that we need the mean to calculate values.

(2) mean = 6, then greatest value = 6+4 = 10, least value = 6-4 = 2
(2) is sufficient. B is the answer.

As for (1), the median has nothing to do with standard deviation, so we can eliminate (1).

oss198 · Answer

You have got the correct answer, however i don't understand it. Standard deviation isn't the  average  of how is spread out the numbers form the mean?

truongvu31 · Answer

I don't get the point of the question. If the question asks for the greatest and the least value within one std, it sounds for me as if the question is asking for REAL values that fall in that range. Since we do not know the set's values, I pick E.

IMO the question should be: What is the greatest possible value and what is the least possible value which falls within one std.

IMO the question should be: What is the greatest possible value and what is the least possible value which falls within one std.

Bunuel · Answer

While I see your point and would agree that the wording is not perfect, notice that the question does not say that the greatest and least values must necessarily be in the set: "what are the greatest and least values that are within one standard deviation of the mean?" So, basically the question asks: what are the the greatest and least numbers which are within a certain distance of the mean.

IanStewart · Answer

I entirely agree with truongvu31 - it's not at all clear what the question even means. It's easy to see why the wording is bad by imagining this instead as a problem solving question, where a specific set was provided. If a question asked:

If the set below:

14, 17, 20, 23, 26

has a standard deviation of 3√2, what are the greatest and least values that are within one standard deviation of the mean?

how would you answer? The mean of the set is 20, and the standard deviation is roughly 4.2, so I'd assume the answer is "23 and 17", since those are the greatest and least values  in the set  within one standard deviation of 20. I don't think it would make any sense to answer this question with "20 + 3√2 and 20 - 3√2". But that's how we're expected to answer the DS question in the OP, if the OA is "B". The answer E seems a much more justifiable answer to me, but in any case, test takers should just ignore the problem, since there are two different and perfectly logical ways to interpret it.

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If the standard deviation of Set Y is 4, what are the

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