Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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 _________________

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. _________________

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.

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.

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.

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. _________________

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' _________________

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

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. _________________