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by mpaudena » Sat Mar 07, 2009 3:15 am
A certain list of data has an average (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 a standard deviation less than d?

A) -6 and 0

B) 0 and 0

c) 0 and 6

D) 0 and 12

E) 6 and 6

Thanks in advance for helping. Please let me know why it works. I think I am missing the standard deviation concept. Taking test in 2 hours. Please no abbreviations as I may not understand it and need to get the quick answer right before going in. Thanks.
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Source: — Data Sufficiency |
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by DanaJ » Sat Mar 07, 2009 4:12 am
Standard deviation is a concept that refers to the average distance between elements of the series and the arithmetic mean. In order to make it smaller, then you should add numbers to the series that are as close to the mean as possible, since that would minimize the distance between the added elements and the mean.
Now, since the mean is 6, you want to add numbers that are as close as possible to 6. This is why E would be your best bet: the distance between 6 and 6 is, obviously, zero, meaning that the new standard deviation will be reduced (look at the standard deviation formula if you want an algebraic explanation)
Is my answer consistent with the OA?

BTW, good luck with your exam!
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