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Set S consists of N elements

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Set S consists of N elements

by amsm25 » Tue Aug 30, 2011 8:33 am

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

1) The mean and the median of the set are equal.
2) The difference between any two elements is equal.
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by saketk » Fri Sep 02, 2011 2:33 pm

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amsm25 wrote:Set S consists of N elements. If N>2 what is the standard deviation of S?

1) The mean and the median of the set are equal.
2) The difference between any two elements is equal.
Statement 1: -- {1,2,3,4,5} -- mean and median equal
Also, {3,3,3,3,3,3} -- Mean and median equal ..

BUT, the SD in both cases is different.. Hence STATEMENT 1 is insufficient.

Statement 2: The difference between any two elements can only be equal when all the elements are same

{1,1,1,1,1,1} or {2,2,2} etc.. Clearly, in each case SD is ZERO.

Hence, STATEMENT 2 is SUFFICIENT.

ANSWER B
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by samyukta » Fri Sep 02, 2011 4:39 pm

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ST 1 : Mean is equal to median which means set has equally spaced elements.

It can be like : 1,2,3,4 or 2,4,6,8. Now both will have different SD.

Insufficient

ST 2: Difference between the elements should be same.... It means all elements are same.

So SD will be zero!!

Pick B
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by wolfmarc » Fri Jan 09, 2015 8:00 am

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Had the second statement been //2) The difference between every two elements is equal.// would the answer have been E?

Because both statements would suggest that we are grappling with an evenly spaced set, of which we ignore the number of elements.

Am I right?
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by Brent@GMATPrepNow » Fri Jan 09, 2015 8:26 am

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wolfmarc wrote:Had the second statement been //2) The difference between every two elements is equal.// would the answer have been E?

Because both statements would suggest that we are grappling with an evenly spaced set, of which we ignore the number of elements.

Am I right?
Your wording "The difference between every two elements is equal" is virtually the same as the original "the difference between any two elements is equal."

If the question stated that the elements (numbers) in set S are arranged in ASCENDING order, and statement 2 was "The difference between any two ADJACENT elements is equal," then the answer would be E

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