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SET- 2006 question...

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by singhpreet1 » Mon Jun 14, 2010 8:34 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

I understand that we do not take -1 and 9, what about the rest of the options B,C,D,E.
Please explain.

Thank you.

Preet
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by Gmat_War » Mon Jun 14, 2010 9:04 am
The mean of the set of 5 numbers is 4.
SD is calculated by finding the diff between the Mean and each of the numbers.Then it is squared and after finding the avg. of the 5 numbers,the non-neg sq.root is calculated.
So in order to find that which set of numbers can be added so that the SD is close to the orig. SD,we need to find numbers which are closer to the mean,i.e. 4.
Option B has 4 and 4 and we can see that adding this two numbers in the set does not affect the original SD since the mean is also 4.Hence SD is unaffected.
IMO B
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by TheGmatTutor » Mon Jun 14, 2010 9:07 am
will result in a new standard deviation that is close to the standard deviation for the original 5 numbers
Did you mean "closest" instead of "close"?

The mean of the original set is 4, and thus answer choice B will result in the biggest decrease in the standard deviation. We can rule this one out.

I believe that in order to answer this question, you actually have to calculate the standard deviation for the original set, which is a very time-consuming process. I've never seen an actual GMAT question that required this. My guess is E.
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by outreach » Mon Jun 14, 2010 10:03 am
i feel the answer as D
4 is avg mean of sets
if variation of set is close then std deviation(SD) r equally close
variation of 5 numbers
=((4-0)^2+(4-2)^2+(4-4)^2+(4-6)^2+(4-8)^2)/5
=(16+4+0+4+16)/5
=40/5
8

variation of 7 numbers should be close to 8
(40+x)/7 should be close to 16

D is nearest

A) (4+1)^2+(4-9)^2=50
B) (4-4)^2+(4-4)^2=0
c) (4-3)^2+(4-5)^2=2
D) (4-2)^2 +(4-6)^2=8
E) (4-0)^2+(4-8)^2=32
singhpreet1 wrote: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

I understand that we do not take -1 and 9, what about the rest of the options B,C,D,E.
Please explain.

Thank you.

Preet
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