kelvind13 wrote:

It looks like you're assuming that all the barrels are the same size, Although it doesn't mention that anywhere in the question.

If the barrels are of different sizes then shouldn't the standard deviation change and is not calculable?

GMATinsight wrote:

Bunuel wrote:

A study involved a total of 6 barrels of a liquid mixture. If the standard deviation of the volume of liquid in the barrels was 10 liters at the start of the study, what was the standard deviation of the volumes of liquid in the barrels at the end of the study?

(1) At the start of the study, the researchers were required to remove 30% from each of the volumes of liquid mixture.

(2) The average (arithmetic mean) volume of liquid mixture in the barrels at the end of the study was 63 liters.

Kudos for a correct solution.

Standard Deviation : Average Deviation of Terms of a set from the Mean value of the SetStatement 1: At the start of the study, the researchers were required to remove 30% from each of the volumes of liquid mixture.Reducing 30% quantity of each barrel will also reduce the deviation of the terms from mean by 30% thereby reducing SD by 30%

SUFFICIENTStatement 2: The average (arithmetic mean) volume of liquid mixture in the barrels at the end of the study was 63 liters Average volume of mixture in the barrels doesn't provide any information on how much the difference in the quantities of mixture is in the barrels. Hence,

NOT SUFFICIENTAnswer: option A

1) If we had assume that all barrels had the same amount of mixture then standard deviation would have been zero. Non Zero standard deviation means that all barrels don't have the same amount of Mixture and the the size of Barrels doesn't matter, all that matters is the amount of Mixture in the barrels

2) The standard deviation of a set doesn't change if a constant is added to/subtracted from each terms of the set

e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1

+10, 2

+10, 3

+10, 4

+10, 5

+10}

Reason: The deviation remains same as before if the constant is added to/Subtracted from each term3) Standard Deviation of the Set changes when a constant term which is not equal to 1 is multiplied with/divides every terms of the set

e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}

Reason: The deviation gets multiplied by or divided by the same constant that every terms is multiplied or divided withI hope it helps!

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