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Source: — Data Sufficiency |
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by GMATGuruNY » Tue Aug 13, 2013 3:51 am
During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?
(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
If every element in a set is increased or decreased by the same CONSTANT, then the standard deviation DOES NOT CHANGE.

If every element in a set is increased or decreased by the SAME PERCENTAGE, then the standard deviation WILL CHANGE BY THE SAME PERCENTAGE.

Statement 1: For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
Since every value was decreased by 30%, the SD at the end of the experiment was 70% of the old SD:
.7(10) = 7.
SUFFICIENT.

Statement 2: The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
No way to determine the SD.
INSUFFICIENT.

The correct answer is A.
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by macattack » Tue Aug 13, 2013 4:13 am
Thank you Mitch, that was the golden rule I was looking for. Decrease by a constant--->SD does not change! Decrease by a percentage--->SD decrease by the same percentage! I am going to make sure I won't forget this one!
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by mgm » Tue Aug 13, 2013 4:14 am
A) Formula for Standard Deviation is sqrt[1/n(xi - mean)^2] ... both the mean and each of the elements are reduced by 30% and hence the SD is reduced by 30%.

B) Mean alone does not provide any insight into the SD change..
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by macattack » Tue Aug 13, 2013 4:16 am
I know but I thought the square in the formula would mess things up but according to Mitch it doesn't and I am sticking to this rule!
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