Answer given in file: A
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?
I. 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.
II. The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
IMO: E
Though, it is true that when a constant is added to all the terms, sd remains same. However, here we don’t know that the volume was same initially, hence 30% (xi) is a constant, thus sd might change.
In this question we apply the basics of standard deviation. SD varies by the same constant with which the original data is multiplied or divided.
I : Here, we can see that since the water removed was 30% of the original the standard deviation. Therefore the data is changed to 0.7 of its original value. Hence, SD is reduced to 0.7 of its original value. Therefore, A or D.
II: I can by no means calculate SD using only mean. Therefore, A is the answer.
