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SD problem

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by sankruth » Tue Jan 22, 2008 4:03 am
A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?

A). -1 and 9
B). 4 and 4
C). 3 and 5
D). 2 and 6
E). 0 and 8

My understanding (dunno if that is right or wrong!) is that SD depends on Range and Average. If any of these two parameters changes, then SD will change. Based on that understanding, I picked A but the solution says D. Can someone please help me with this one?
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by StarDust845 » Tue Jan 22, 2008 5:52 am
I don't agree with your solution or with the OA.

If we think about it, for a set of numbers, what elements added to the set will modify the SD by the least amount?

The added numbers in the given question all increase the total value of the set by the same amount 8. That means, the numbers nearest to the mean of the original set will give us the least change in SD.

Hence the answer must be 4 & 4. i.e. B

Calista.
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by Stuart@KaplanGMAT » Tue Jan 22, 2008 6:38 am
Where is this question from?

I've never seen that detailed a standard deviation question on the actual GMAT.
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by cris » Tue Jan 22, 2008 6:41 am
Calista I thought the same thing and chose B too.

But if you rethink it you will see that is indeed D the correct answer.

By chosing 4 and 4 the SD is changing a lot more that if you chose 2 and 6.
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by StarDust845 » Tue Jan 22, 2008 7:30 am
cris wrote:Calista I thought the same thing and chose B too.

But if you rethink it you will see that is indeed D the correct answer.

By chosing 4 and 4 the SD is changing a lot more that if you chose 2 and 6.
If what you are saying is true, there is nothing to "think" here. We just have to solve and calculate the SD. That makes it a lousy question, but I got it wrong.

So why is my (our) analysis wrong?

Calista.
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by sankruth » Tue Jan 22, 2008 7:39 am
There is a document with 100 difficult math questions on BTG, section GMAT Math.

Less than a week to go and it is not doing much good to my confidence though... :cry:
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