list of 102 data with SD < d

[alivapriyada]

A certain list of 100 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 standard deviation less than d?

A) -6 and 0
B) 0and 0
C) 0and 6
D) 0 and 12
E) 6 and 6

OA later
Please Explain.....

[Brian@VeritasPrep]

Hey alivapriyada,

I like the setup of this question a lot! The GMAT tests Standard Deviation exclusively in a conceptual way - you're not responsible for calculating it, but you need to know what it represents.

A lot of what it represents can be determined just by thinking of its name. "Standard Deviation" means essentially "the typical amount that data deviates" - standard deviation measures the variance between the data points and the average.

Here, we only know two things:

1) The average is 6.

2) The standard deviation is positive. This should seem almost like a nonissue, but it's actually quite critical - standard deviations cannot be negative, but if there is NO deviation the standard deviation is 0. Here, the fact that the standard deviation > 0 means that there IS some deviation (not all of the data points are 6).

We don't, however, know what that deviation is. It could be that the data points are all 6, except for a 6.1 and a 5.9. Or it could be that the data points are spread all over the place.

The ONLY number that we know will reduce the standard deviation is 6 itself. If more data points are exactly at 6, then that means that the "typical deviation" is reduced. The more 6s in the data, the less frequently the data typically strays from the mean, and so therefore the data points 6 and 6 will reduce the standard deviation. Therefore, the correct answer is E.

When thinking about standard deviation, try to keep it conceptual, as it's much easier to think about that way, and that's all you're required to know.

[scorpionz]

A certain list of 100 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 standard deviation less than d?

A) -6 and 0
B) 0and 0
C) 0and 6
D) 0 and 12
E) 6 and 6

OA later
Please Explain.....

Yep..Got to be E..Brian has explained it brilliantly (as always) above..

My two cents...
SD is a measure of how far or how spread apart the individual data elements are from the mean of the set. In any example, the best way to reduce the SD (if not already 0) of the entire set would be to introduce more elements which equal the mean of the existing set. This ensures that the mean doesn't change but the no. of elements is increasing which in turn reduces the SD..

The same example above can be rephrased to change 6 to any no. The answer to such a question will always be that no.

Hope this helps!!

Cheers!