344. During an experiment, some water was removed from each of the 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% 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.
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344. During an experiment, some water was removed from each
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puneetkhurana2000
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Initially... 100 = ((a-x)^2 + (b-x)^2 + (c-x)^2 + ... (f-x)^2 )/6 ..eqn(1) where x is the mean and a,b,c...f are the initial volumes of water.
Statement 1) New a1 = .70*a and similarly every new volume is 70% of the initial volumes.
New SD becomes ((.70*a-x)^2 + (.70*b-x)^2 + (.70*c-x)^2 + ... (.70*f-x)^2 )/6, we can find New SD as we know the values from eqn(1)(Take out common factors and New SD can be found out).
Sufficient!!!
Statement 2) New Mean(x1) = 63, but no information about new a,b,c...f. Not Sufficient!!!
Answer A.
Statement 1) New a1 = .70*a and similarly every new volume is 70% of the initial volumes.
New SD becomes ((.70*a-x)^2 + (.70*b-x)^2 + (.70*c-x)^2 + ... (.70*f-x)^2 )/6, we can find New SD as we know the values from eqn(1)(Take out common factors and New SD can be found out).
Sufficient!!!
Statement 2) New Mean(x1) = 63, but no information about new a,b,c...f. Not Sufficient!!!
Answer A.
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(1) It is given that 30% of the volume of water is removed from all the tanks so standard deviation remains same; SUFFICIENT.varun289 wrote:344. During an experiment, some water was removed from each of the 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% 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.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons does not help in finding the standard deviation of the volumes of water in the tanks at the end of the experiment; NOT sufficient.
The correct answer is A.
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If every data point is increased or decreased by the same CONSTANT, then the standard deviation DOES NOT CHANGE.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 data point 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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