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GMAT Diagnostic Test Question 17 Field: statistics Difficulty: 650

Set S consists of N elements. If N>2, what is the standard deviation of S?

(1) The mean and median of the set are equal (2) The difference between any two elements of the set is equal

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient
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Statement 1: If the mean and median of the set is positive, the Standard deviation could be anything. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the Standard deviation isn’t same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So Standard deviation is 0. Suff. So B is the answer.
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Statement 1: If the mean and median of the set is positive, the Standard deviation could be anything. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the Standard deviation isn’t same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So Standard deviation is 0. Suff. So B is the answer.

Please elaborate on your rationale for answer B as I am not sure I follow your statement 2, i.e. the difference between any two elements of the set is equal? The only way for stdev to be zero is if all elements are of equal value i.e. 5, 5, 5 thus mean 5, median 5 and stdev ^ 2 = [ ( 5 - 5)^ 2 + ( 5 - 5)^ 2 + ( 5 - 5)^ 2 ] / 3 = 0.

Statement 1: If the mean and median of the set is positive, the Standard deviation could be anything. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the Standard deviation isn’t same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So Standard deviation is 0. Suff. So B is the answer.

Please elaborate on your rationale for answer B as I am not sure I follow your statement 2, i.e. the difference between any two elements of the set is equal? The only way for stdev to be zero is if all elements are of equal value i.e. 5, 5, 5 thus mean 5, median 5 and stdev ^ 2 = [ ( 5 - 5)^ 2 + ( 5 - 5)^ 2 + ( 5 - 5)^ 2 ] / 3 = 0.

The only way to have equal difference between any two elements is to have all elements equal. If so, then SD is 0.

Statement 1: If the mean and median of the set is positive, the Standard deviation could be anything. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the Standard deviation isn’t same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So Standard deviation is 0. Suff. So B is the answer.

Please elaborate on your rationale for answer B as I am not sure I follow your statement 2, i.e. the difference between any two elements of the set is equal? The only way for stdev to be zero is if all elements are of equal value i.e. 5, 5, 5 thus mean 5, median 5 and stdev ^ 2 = [ ( 5 - 5)^ 2 + ( 5 - 5)^ 2 + ( 5 - 5)^ 2 ] / 3 = 0.

The only way to have equal difference between any two elements is to have all elements equal. If so, then SD is 0.

You're absolutely right about the statement in red. However, this is also the reason why S1 alone is not sufficient. If standard deviation can be anything, you can't know what the SD is exactly. Hence, B.

varun2410 wrote:

Ans can not be B: If the mean and median of the set is positive, the Standard deviation could be anything

any statment itself can not be wrong ,if mean and median are same then set itself consist of that kind of number only.

Set S consists of N elements. If N>2, what is the standard deviation of S?

(1) The mean and median of the set are equal (2) The difference between any two elements of the set is equal

Second statement is only possible if the set has same element. Standard deviation actually is the avg of the differences of each element with the avg. sd = sqrt(sum(diff of each element with avg^2)/N) Since difference between any two elements is equal any number - avg = 0 since all the elements are of same value and hence sd is zero so, B is the answer.
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Statement (1) says "The mean and median of the set are equal"

Why is everyone referring to Statement (1) as "...the mean and median of the set is positive"

These are 2 completely different things no?

"The mean and median of the set are equal" => all elements in the set are the same => SD = 0 => Statement (1) also sufficient => Answer is D.

Am I missing something?

The mean and median of a set can be equal for two cases: (1) All elements are same ==> SD =0 (2) Elements are consecutive numbers ==> SD will vary. So, statement (1) will be NSF.

if the set consists of N elements which refers to the number has in the set....right? if this is true thn N<2...tht means N= 1 or 0 so i think each statement is enough... 'D'
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if the set consists of N elements which refers to the number has in the set....right? if this is true thn N<2...tht means N= 1 or 0 so i think each statement is enough... 'D'

On the document of what to memorize. Standard deviation can be found by taking the absolute value of the median-mean. If these two are the same value wouldn't that automatically make the SD 0. So A would be sufficient? Sorry for the inconvenience.

You're absolutely right about the statement in red. However, this is also the reason why S1 alone is not sufficient. If standard deviation can be anything, you can't know what the SD is exactly. Hence, B.

varun2410 wrote:

Ans can not be B: If the mean and median of the set is positive, the Standard deviation could be anything

any statment itself can not be wrong ,if mean and median are same then set itself consist of that kind of number only.

ans D

i think from second ...all equal so sd is 0 seems to work (still testing possiblities) but i think in gmat in question such as this which asks "what is standard deviation sd?" one needs to be able to find a value(though he doesnt need to show the actual value-so i said 'able to' and saying sd can be any thing is no good in gmat ....that i what i have learned so far... sd can be any thing means it can take mulitiple values which means it is not sufficient... so if we with your logic B cannot be answer

On the document of what to memorize. Standard deviation can be found by taking the absolute value of the median-mean. If these two are the same value wouldn't that automatically make the SD 0. So A would be sufficient? Sorry for the inconvenience.

Is that so?? Correct me if I am wrong... Standard deviation is 0 incase all the elements in a set are the same. In this case the mean and median both will be the same. However the vice-versa may not be true. Mean and median are the same in those cases also in which the elements in the set are in some arithmetic series. But the standard deviation in those cases is not zero. Also, the Standard devaiation varies with the values of the elements in the set.

tingle15: you're right. You can be sure that Mean = Median when SD is 0, but you can't be sure that SD is 0 only on the basis of Mean = Median.
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