Is the Standard Deviation of Set S Greater than the Standard Deviation of Set T? GMAT Data Sufficiency

Question: Is the standard deviation of set S greater than the standard deviation of set T?

1. The range of the set S greater than the standard deviation of set T
2. The mean of set S is greater than the mean of set T

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“Is the standard deviation of set S greater than the standard deviation of set T?”– is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken f0rom the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

Standard deviation shows how many variations there is from the mean, how wide spread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standards deviation indicates that the data are spread out over a large range of values.

1. The range of set S is greater than the range of set T. This implies that the biggest and smallest numbers in S are more widespread than the biggest and smallest numbers in T. but what about the other numbers of these sets.
   SD of {0,10} is greater than SD of {0,9}, but SD of {0,1,2,3,4,5,6,7,8,9,10} is less than SD of {0,9}.
   Hence this statement is not sufficient.
2. The mean of set S is greater than the mean of set T. Info about the mean is totally useless to get widespread the given sets are.
   Hence this statement is not sufficient.

(1) + (2) Statement (2) gives absolutely no new info for (!), so even taken together they are still insufficient to answer the question.

Correct Answer: E

Approach Solution 2:

We will understand this question by considering two examples:
S is {-4,-3,-2,-1,0,1,2,3,4,5,6} and T is {-4,4}.

Meets restriction of (!) and (2), and the answer to the prompt is no.
S is {-4,6} and T is {-4,4}.

Meets restrictions of (1) and (2), and the answers to the prompt is yes.
Hence the statements are insufficient.

Correct Answer: E

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