Question on SD

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sankruth: Master | Next Rank: 500 Posts; Posts: 195; Joined: Sun Oct 21, 2007 4:33 am; Thanked: 10 times

Question on SD

by sankruth » Wed Jan 16, 2008 12:03 pm

If M is a negative integer and K is a positive integer, which of the following could be the Standard Deviation of the set {-7, -5, -3, M, 0, 1, 3, K, 7}

I. -1.5
II -2
III 0

A - I only
B - II only
C - III only
D - I and III only
E - None

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Source: Beat The GMAT — Problem Solving | Wed Jan 16, 2008 12:03 pm

StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Wed Jan 16, 2008 12:09 pm

Is the answer E?

Calista.

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sankruth: Master | Next Rank: 500 Posts; Posts: 195; Joined: Sun Oct 21, 2007 4:33 am; Thanked: 10 times

by sankruth » Wed Jan 16, 2008 12:25 pm

StarDust845 wrote:Is the answer E?

Calista.

Sorry, I forgot to ask the main question... Is there a way to solve it in under 2 minutes?

By the way E is correct!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: Question on SD

by Stuart@KaplanGMAT » Wed Jan 16, 2008 12:33 pm

sankruth wrote:If M is a negative integer and K is a positive integer, which of the following could be the Standard Deviation of the set {-7, -5, -3, M, 0, 1, 3, K, 7}

I. -1.5
II -2
III 0

A - I only
B - II only
C - III only
D - I and III only
E - None

Just curious - where is this question from? I've never seen a GMAT question that asked the test taker to calculate SD.

On the other hand, we don't actually need to do any calcuations to answer this question, we just need to understand how SD works.

SD is a measurement of how spread out the members of a set are. Since SD really measures distance, there's no such thing as a negative SD.

Further, unless all the members of the set are identical, the SD will always be greater than 0.

So, we can't have negative SD, statements I and II are out. Some of the members of the set are different, so statement III is out. Pick (e), none of the above.