GMAT Prep question about standard deviation

My answer is C. If this is correct, I will give the explanation.

rossmj wrote: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 begining of the experiment was 10gal. what was the standard deviation of the volumes of the water in the tanks at the end of the experiment?
1) For each tank 30% of the volume of the water that was in the tank at the begining was removed during the experiment.
2) The average volume of water in the tanks at the end of the experiment was 63 gallons

I understand the answer now but a discussion about the necessary info and what changes standard deviation would be greatly appreciated.

IMO A

1. In given set of data points, when a particular value is subtracted from or added to data points, SD doesnt change as the data points and mean increase by the same magnitude. For example
2 4 6

Mean: 4

SD is approximately proportional to difference between mean and data points

Difference between datapoints and mean

-2,0,2---I

Subtract constant 1 from each data point

1 3 5

Mean: 3

Difference -2,0,2-II


From I and II, difference between mean and datapoint remains same before and after subtraction and hence SD will not change

In this case, as 30% is removed, Sd wont change. SD after removing water=10gal

2. we neither know how much the data points change nor do we know the individual datapoints to caculate average before.


IMO A

agree with iamcste on A, except that the SD will not remain unchanged, it will be 10*0.7=7 (all the tanks are reduced by 30%, ie the final volume of each tank becomes 0.7 times the opening voume)

SD doesnt change as the data points and mean increase by the same magnitude, but SD changes when the data points are multiplied/divided by the same constant. (the SD is multiplied/divided accordingly)

scoobydooby wrote:agree with iamcste on A, except that the SD will not remain unchanged, it will be 10*0.7=7 (all the tanks are reduced by 30%, ie the final volume of each tank becomes 0.7 times the opening voume)

SD doesnt change as the data points and mean increase by the same magnitude, but SD changes when the data points are multiplied/divided by the same constant. (the SD is multiplied/divided accordingly)

I thought about this case too: even with this, we are sufficient to answer the question.

Can you clarify one thing: I agree with that datapoints will be scaled by 0.7 after removal of 30% but dont you think "removing" somthing is more closer to "subtraction" operation than multiplication operation. wanted to clarify in case this comes as a PS qtn.

I am getting an answer of A as SD will remain same

B does not tell us anything about individual quantity.
What is OA?

iamcste wrote:

scoobydooby wrote:agree with iamcste on A, except that the SD will not remain unchanged, it will be 10*0.7=7 (all the tanks are reduced by 30%, ie the final volume of each tank becomes 0.7 times the opening voume)

SD doesnt change as the data points and mean increase by the same magnitude, but SD changes when the data points are multiplied/divided by the same constant. (the SD is multiplied/divided accordingly)

I thought about this case too: even with this, we are sufficient to answer the question.

Can you clarify one thing: I agree with that datapoints will be scaled by 0.7 after removal of 30% but dont you think "removing" somthing is more closer to "subtraction" operation than multiplication operation. wanted to clarify in case this comes as a PS qtn.

well here it is a substraction in disguise

as SD- 0.3*SD = 0.7*SD

HTH.

iamcste wrote:

scoobydooby wrote:agree with iamcste on A, except that the SD will not remain unchanged, it will be 10*0.7=7 (all the tanks are reduced by 30%, ie the final volume of each tank becomes 0.7 times the opening voume)

SD doesnt change as the data points and mean increase by the same magnitude, but SD changes when the data points are multiplied/divided by the same constant. (the SD is multiplied/divided accordingly)

I thought about this case too: even with this, we are sufficient to answer the question.

Can you clarify one thing: I agree with that datapoints will be scaled by 0.7 after removal of 30% but dont you think "removing" somthing is more closer to "subtraction" operation than multiplication operation. wanted to clarify in case this comes as a PS qtn.

hi iamcste,
yes we are removing a portion of each tanks volume , but in effect we are scaling each tank down by a factor of 0.7
v1-0.3v1=0.7v1 as cubicle-bound-misfit has mentioned.

this 0.3v1 is not a constant across the board, it varies for each tank. if it said x litres were removed from each tank, then it would have been a subtraction operation and SD would have remained unchanged.