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by crackgmat007 » Thu Jul 16, 2009 7:45 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 same as 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

Pls explain
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by cata1yst » Thu Jul 16, 2009 7:57 am
I am stuck between A and B.

I guess I will choose B. Not sure why though.
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by yogami » Thu Jul 16, 2009 8:11 am
Well I am not sure whats wrong with my calc. None of the answers actually give an SD the same as the original
The original SD is sqrt(8)
Because it is sqrt(((4 - 0)^2 + (4 - 2)^2 + (4 - 4)^2 + (4 - 6)^2 + (4 - 8)^2))/5)
which is sqrt(40/5) = sqrt(8)
Now the denominator for the sd within the sqrt for every option has to be 7 because you are adding two more numbers in the set
And for SD to remain the same the numerator has to be 7*8 i.e 56. Now which of the options yields a numerator of 56??. None
So I am not sure whats going on
200 or 800. It don't matter no more.
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by abhinav85 » Thu Jul 16, 2009 10:08 am
IMO B.

5 nos are 0 2 4 6 8.

So we can see that every value is 2 units apart.

And the median is 4.

And if we will add 4 and 4.the SD will not change.

0 2 4 4 4 6 8. In this median remain the same(4).
and equal value on both the sides to the median.
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by Ian Stewart » Thu Jul 16, 2009 10:32 am
None of the answers will keep the standard deviation the same. The original question asks which pair of values will change the standard deviation least, not which will make the standard deviation identical. In any case, it's not the kind of problem you need to be concerned about if you're preparing for the GMAT, since there's no straightforward way to answer it without using the std deviation formula, something that's not required on any real GMAT problems.
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