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A certain list of 100 data has an avarage (arithmetic mean)

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A certain list of 100 data has an avarage (arithmetic mean) [#permalink] New post 22 Mar 2008, 03:58
A certain list of 100 data has an avarage (arithmetic mean) of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 102 data with standard deviation less then d?

1. -6 and 0
2. 0 and 0
3. 0 and 6
4. 0 and 12
5. 6 and 6

Can someone point me where I can learn more about standard deviation?
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Re: Standard deviation [#permalink] New post 22 Mar 2008, 05:50
I think answer is E.

SD is measure of deviation of data from mean/average. Given that average is 6. Also given that D is +ve, means there is some sort of deviation.

If you add values, which are same as mean/average that will lower the deviation (because you are adding two more values to the series which are contributing to zero deviation, which means you are adding 2 values in series without increasing deviation thereby deviation will decrease).

As 6, and 6 is same as mean/average, so they will lower the deviation.
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Re: Standard deviation [#permalink] New post 22 Mar 2008, 06:47
E - deviation is minimum (zero) for these values.

Try this -> http://davidmlane.com/hyperstat/A16252.html (you don't the material on second page for GMAT).
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Re: Standard deviation [#permalink] New post 22 Mar 2008, 07:59
OA is E.
Thanks for the explanations.
Re: Standard deviation   [#permalink] 22 Mar 2008, 07:59
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A certain list of 100 data has an avarage (arithmetic mean)

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