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Standard deviation question

by Adi_Pat » Tue Sep 07, 2010 10:25 am
During an expt. water is removed from each of 6 tanks. If the standard deviation of the volume of water in each tank before at the start is 10 gallons what will the standard deviation be at the end of the experiment

1) 30% of volume of water is removed from each tank during the expt.
2) the average volume at the end of the experiment was 63 gallons.

OA A

Any general comments of calculating standard deviation in this type of question - what stumped me with the OA is that since we dont know the exact amounts of the 6 tanks - a 30% change would mean a different change in volume for each tank - so how do we calculate the SD. Help !
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by Gurpinder » Tue Sep 07, 2010 1:36 pm
imo (A)

the point in such a question is not knowing the EXACT amounts but knowing the average and discrepancies of each values.

(1). we know that 30% is removed from EACH tank.

so if each tank has 10 g of water. 30% removed from each. so 7g of water in each tank.
therefore the SD = 0.

Hence sufficient.


(2). total was 63 gallons but we dont know the discrepancy between each of the tanks.

hence insufficient.
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by Adi_Pat » Wed Sep 08, 2010 7:52 am
Gurpinder wrote:imo (A)

the point in such a question is not knowing the EXACT amounts but knowing the average and discrepancies of each values.

(1). we know that 30% is removed from EACH tank.

so if each tank has 10 g of water. 30% removed from each. so 7g of water in each tank.
therefore the SD = 0.

Hence sufficient.


(2). total was 63 gallons but we dont know the discrepancy between each of the tanks.

hence insufficient.

it says the standard deviation of the volume of water in each tank is 10 gallons..not the volume in each tank....
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by Gurpinder » Wed Sep 08, 2010 7:57 am
Adi_Pat wrote:
Gurpinder wrote:imo (A)

the point in such a question is not knowing the EXACT amounts but knowing the average and discrepancies of each values.

(1). we know that 30% is removed from EACH tank.

so if each tank has 10 g of water. 30% removed from each. so 7g of water in each tank.
therefore the SD = 0.

Hence sufficient.


(2). total was 63 gallons but we dont know the discrepancy between each of the tanks.

hence insufficient.

it says the standard deviation of the volume of water in each tank is 10 gallons..not the volume in each tank....
yes. but read the question carefully!

SD=10 for vol of water in EACH tank.
if 30% is removed from EACH tank, the SD will NOT change because you are removing the EXACT amount from EACH tank.
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by beatthegmatinsept » Wed Sep 08, 2010 8:08 am
Gurpinder wrote: yes. but read the question carefully!

SD=10 for vol of water in EACH tank.
if 30% is removed from EACH tank, the SD will NOT change because you are removing the EXACT amount from EACH tank.
But 10% of different numbers can vary.
For example:
100 * 10% = 10, Remaining water = 90
90 * 10% = 9, Remaining water = 81
110 * 10% = 11, Remaining water = 99
95 * 10% = 9.5, Remaining water = 85.5
So, the fact that all of these 4 examples, leave you with numbers that are within 10 SD of each other, is that enough to mark this choice as sufficient?
(We don't know what the mean is, so we can only assume).
Is my approach close to the right approach at all here?
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by debmalya_dutta » Wed Sep 08, 2010 8:44 am
Adi_Pat wrote:During an expt. water is removed from each of 6 tanks. If the standard deviation of the volume of water in each tank before at the start is 10 gallons what will the standard deviation be at the end of the experiment

1) 30% of volume of water is removed from each tank during the expt.
2) the average volume at the end of the experiment was 63 gallons.

OA A

Any general comments of calculating standard deviation in this type of question - what stumped me with the OA is that since we dont know the exact amounts of the 6 tanks - a 30% change would mean a different change in volume for each tank - so how do we calculate the SD. Help !
I think everyone has stated what the right answer is

Why is B incorrect ...
It gives me the average volume at the end of experiment ... and the question stem tells me that the standard deviation is within 10 gallon at the start ... ..However , to determine the standard deviation at the end of the experiment, I would need to know how have the volumes in the individual jars changed ... If they have changed uniformly, it means that the standard deviation is still the same ... If it has been changed randomly ...then I cannot comment on what the final SD is ...right
For example ..take 3 jar
110, 100, 90 (start of experiment) - Mean = 100

Now , say the mean was 90 at the end of the experiment ..

So the jars could hold 100, 90, 80(mean is 90, SD=10) or the jars could hold 105, 90 , 75(Mean = 90 and SD= 15)
So , I need to know how much water was removed from each of the jars to really comment on whether the SD has changed after the experiment

Option A tells me that equal amounts were removed from each of the jars ..so at the end , the SD will remain unchanged. Key take-away is to view SD as deviation in the set of values around the mean i.e how far are the values from the mean
@Deb
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by Adi_Pat » Wed Sep 08, 2010 9:41 am
debmalya_dutta wrote:
Adi_Pat wrote:During an expt. water is removed from each of 6 tanks. If the standard deviation of the volume of water in each tank before at the start is 10 gallons what will the standard deviation be at the end of the experiment

1) 30% of volume of water is removed from each tank during the expt.
2) the average volume at the end of the experiment was 63 gallons.

OA A

Any general comments of calculating standard deviation in this type of question - what stumped me with the OA is that since we dont know the exact amounts of the 6 tanks - a 30% change would mean a different change in volume for each tank - so how do we calculate the SD. Help !
I think everyone has stated what the right answer is

Why is B incorrect ...
It gives me the average volume at the end of experiment ... and the question stem tells me that the standard deviation is within 10 gallon at the start ... ..However , to determine the standard deviation at the end of the experiment, I would need to know how have the volumes in the individual jars changed ... If they have changed uniformly, it means that the standard deviation is still the same ... If it has been changed randomly ...then I cannot comment on what the final SD is ...right
For example ..take 3 jar
110, 100, 90 (start of experiment) - Mean = 100

Now , say the mean was 90 at the end of the experiment ..

So the jars could hold 100, 90, 80(mean is 90, SD=10) or the jars could hold 105, 90 , 75(Mean = 90 and SD= 15)
So , I need to know how much water was removed from each of the jars to really comment on whether the SD has changed after the experiment

Option A tells me that equal amounts were removed from each of the jars ..so at the end , the SD will remain unchanged. Key take-away is to view SD as deviation in the set of values around the mean i.e how far are the values from the mean

OK !!! so lets consider the 3 jar example again...

we are given the standard deviation is 10 of the volume of each jar... so we can assume (70,80,90) or (90,100,110) etc...
if we are told that the volumes of each decrease by 30%...depending on our assumption we would get the volumes at the end are (70-21,80-24,90-27) = ( 49,56,63 ) or ( 90-27,100-30,110-33 )= (63, 70,77)

but the SD is still not 10..so unless we know the volumes at the start how do we calculate the SD at the end...???
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by Stuart@KaplanGMAT » Wed Sep 08, 2010 10:18 am
Adi_Pat wrote:During an expt. water is removed from each of 6 tanks. If the standard deviation of the volume of water in each tank before at the start is 10 gallons what will the standard deviation be at the end of the experiment

1) 30% of volume of water is removed from each tank during the expt.
2) the average volume at the end of the experiment was 63 gallons.


Any general comments of calculating standard deviation in this type of question - what stumped me with the OA is that since we dont know the exact amounts of the 6 tanks - a 30% change would mean a different change in volume for each tank - so how do we calculate the SD. Help !
For the GMAT, you don't need to know how to calculate standard deviation ("SD"); you may need to know what's required to calculate SD or what SD generally is.

To calculate the SD of a set, you need 2 pieces of info about the set:

1) the number of terms; and
2) the exact spacing of all terms.

Let's apply that information to this question:

From the stem, we know that SD = 10 and there are 6 terms.

From (1), we know that 30% of the water is removed from each tank. Similarly, we know that 70% of the water remains in each tank; in other words, the volume of each tank is multiplied by .7.

Accordingly, we know that the new spacing between each pair of terms is .7 of what it used to be. For example, if tank 1 originally had 20 gallons of water and tank 2 originally had 25 gallons of water, there used to be a "spread" of 5 gallons. After the change, there will be a spread of .7(5) = 3.5 gallons.

Since we know the new spacing relative to the old spacing, it's possible to calculate the SD of the new set (the calculation might be incredibly complicated, but that doesn't affect whether it can be made).

Therefore, (1) is sufficient alone.

Not going to worry about (2) - lots of good discussion already!
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