Hey Guys,
I'm a little bit confused by this question, and by the conversation around it. If every set of numbers in a group is multiplied by a constant, the standard deviation CAN change. So I don't quite see how (A) would be the answer here.
To illustrate, let's look at a sample where all 6 tanks have the same amount of water in them: 100, 100, 100, 100, 100, 100
If these all go down by 30%, the standard deviation doesn't change: 70, 70, 70, 70, 70, 70
But if the sample has a bunch of different values, the standard deviation WILL change: 10, 20, 30, 40, 50, 60
If these all go down by 30%, they become: 7, 14, 21, 28, 35, 42
The amount that these numbers differ from the mean IS smaller, so the SD is smaller.
I realize that my examples don't match the given information (the set has an SD of 10 to begin with), but what you'll find is that creating a standard deviation of 10 can be done with really big numbers (10,000,000) or in the range of numbers like 100. Depending on how big the numbers are, the effect of multiplying all the numbers in the set by .7 will shrink the SD by a different amount. In other words, you can't solve for the thing.
I'm definitely open to argument; this question has been posted so badly (full of weird typos and such), that I could be missing something...
-t
P.S. The point made by Alexander, that multiplying by a fixed number is the same as subtracting a fixed number, is incorrect. However, he is correct that if you were to add or subtract a fixed number to the tanks, that would NOT affect the SD.
Tommy Wallach, Company Expert
ManhattanGMAT
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