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experiment

by GmatKiss » Mon Aug 15, 2011 3:42 am
During an experiment,some water was removed from each of 6 water tanks.If the SD of the volumn of the water in the tank at the begining of the experiment was 10 gallons,what was the SD of the volumns of water in the tank at the end of the experiment??

A--For each tank,30%of the volumn of water that was in the tank at the begining of the experiment was removed during the experiment.

B--The average volumn of water in the tank at the end of the experiment was 63 gallons.
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by sumgb » Mon Aug 15, 2011 11:49 am
Answer must be A. Here's why -

std dev = sq rt{summation of (mean - term)^2/no of terms}

stmnt 1 tells us that a constant 30% is removed from each tank. This means that the avg reduces by 30%. this would also mean [summation of (mean - term) reduces by 30%. we know std dev from initial conditions, we know no of terms, we can find out [summation of (mean - term) in new conditions. Hence we can find out the new std dev. suff. (no need to calculate here)

cross off B C E

stmnt 2 tells us the avg vol of water in the tank at the end of exp, we have no means of knowing the reduction factor here. so insuff.

cross off D

Answer: A
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by force5 » Mon Aug 15, 2011 12:49 pm
+ 1 to A.
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by gmatboost » Wed Aug 17, 2011 3:01 pm
There seem to be a lot of questions about Standard Deviation (more than I feel it deserves, since it is a rare topic), so I decided to put together a summary blog post about SD on the GMAT:

https://blog.gmatboost.com/2011/08/17/me ... deviation/
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by alexander.vien » Thu Jan 17, 2013 4:04 pm
How to calculate SD will not be tested on the GMAT - in many cases you don't even need to know the general formula - only how SD changes when things are added/subtracted from a set.

That being said, this question requires no calculation.

You have 6 water tanks (kind of like saying you have 6 terms in a set) - and the SD of the volume in each tank is 10. Well we don't know how much water is in each tank - but do we really need to know? The question is asking what the SD will be once the experiment is over.

Statement 1 - From this statement, we know what is happening in the experiment - the amount of water in each tank is being removed (hint: this is kind of like subtracting a fixed number from each of the numbers in a set). For example, if we have a set of 6 numbers [1, 2, 3, 4, 5, 6] and we subtract the same amount from each number (say, 1), then are new set is [0, 1, 2, 3, 4, 5]. Did the SD change? The mean changed, and the median changed, but is the distance around the mean different? No, it's still evenly spaced. So, if we're removing the same amount from each tank, then the SD will not change. Statement A is SUFFICIENT. (If on the other hand, we added 2 tanks, with varying volumes, it would be a different story).

Statement 2 - As stated above, we don't really care about the amount that's in each tank. This statement doesn't define what the experiment is, or what was changed, and is somewhat irrelevant. So, INSUFFICIENT.

The answer is A
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by Tommy Wallach » Fri Jan 18, 2013 12:28 am
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.
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