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standard deviation

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standard deviation

by hpgmat » Thu Dec 10, 2009 5:56 pm
a certain list of 100 data has and average of 6 and a standard deviation of d where d is positive. which of the following paris of data , when added to the list , must result in a list of 102 data with standard deviation less than d

-6 and 0
0 and 0
0 and 6
0 and 12
6 and 6

please explain
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by ace_gre » Fri Dec 11, 2009 2:57 pm
Is it 6 and 6?

Standard deviation d=( Summation (Xi-mean)^2/n) ^1/2.

When Xi=6, Xi-mean=0. Only n increases to n+2 ,while numerator does not change. Hence d decreases.
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by Testluv » Sat Dec 12, 2009 10:29 am
Yes, the answer is definitely choice E but there is no need to recall the formula. In fact, you don't need to memorize the standard deviation formula for the GMAT exam. You just need to know the concept. Standard deviation measures the standard "spreading out" of data from the center or mean.

So this set's standard deviation is zero: {5, 5, 5, 5,}

and this set will have a relatively small standard deviation: {4, 4, 5, 6, 6}

while this set's standard deviation will be larger: {1, 1, 5, 9, 9}

This question tells us that the average is 6, and that the standard deviation is d. We need to add in two numbers that will decrease the standard deviation: in order to do this, we need to make the center or mean larger than it was before. We need more 6's.

Choose E.
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