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# The Department of Environmental Protection measured the volume of wate

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Math Expert
Joined: 02 Sep 2009
Posts: 55169
The Department of Environmental Protection measured the volume of wate  [#permalink]

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09 Feb 2017, 10:46
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Difficulty:

65% (hard)

Question Stats:

48% (01:18) correct 52% (01:15) wrong based on 121 sessions

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The Department of Environmental Protection measured the volume of water in 10 similarly sized reservoirs in State X and found that the standard deviation of their volumes at the start of the year was a certain value. Was the standard deviation of those 10 volumes the same at the end of the year?

(1) During the year the volume of water in each reservoir decreased by 5 million cubic gallons.

(2) During the year the volume of water in each reservoir decreased by 20%.

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Joined: 24 Apr 2016
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Re: The Department of Environmental Protection measured the volume of wate  [#permalink]

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09 Feb 2017, 14:53
2
Statement 1: Decreasing the number in a set by a constant, does not change the Standard Deviation of the set of numbers.

In this case since the amount of water decreased in each tank is a constant value. The standard deviation does not change. So we know that Standard Deviation was same at the end of the year.

Statement 1 is sufficient.

Statement 2: In this case the amount decreased is 20% of each tank, which is a variable amount for each tank (depending on the water in each tank. Now if each tank had the same quantity of water, then decrease would be constant and the Standard Deviation would remain the same. But the tanks may also have different quantities of water, resulting in a different Standard Deviation at the end of the year. Since we do not have that information about the quantity of water in each tank, This Statement is not sufficient.

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Re: The Department of Environmental Protection measured the volume of wate  [#permalink]

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09 Feb 2017, 23:42
(1) - Adding/Subtracting a number from all elements of set will not change the deviation of the set. - Sufficient

(2) - Multiplying/Dividing a number from all elements will change the SD.

But if the original SD of the set was 0(all numbers in set were same), then multiplying/dividing will not have any effect on the SD.

Mathematically, if the old SD was d and if a number k is multiplied to every number of the set then the new SD will be kd. If d is 0 kd will also be 0. So not sufficient

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Joined: 03 Dec 2016
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Re: The Department of Environmental Protection measured the volume of wate  [#permalink]

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09 Apr 2018, 12:42
quantumliner wrote:
Statement 1: Decreasing the number in a set by a constant, does not change the Standard Deviation of the set of numbers.

In this case since the amount of water decreased in each tank is a constant value. The standard deviation does not change. So we know that Standard Deviation was same at the end of the year.

Statement 1 is sufficient.

Statement 2: In this case the amount decreased is 20% of each tank, which is a variable amount for each tank (depending on the water in each tank. Now if each tank had the same quantity of water, then decrease would be constant and the Standard Deviation would remain the same. But the tanks may also have different quantities of water, resulting in a different Standard Deviation at the end of the year. Since we do not have that information about the quantity of water in each tank, This Statement is not sufficient.

Wouldn't Statement 2 also be sufficient to answer the question.

Given that all volumes are reduced by the same percentage amount, the SD would also reduce by a particular amount and would never be the same as the starting standard deviation
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Re: The Department of Environmental Protection measured the volume of wate  [#permalink]

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22 Apr 2018, 01:05
1
Novice90 wrote:
quantumliner wrote:
Statement 1: Decreasing the number in a set by a constant, does not change the Standard Deviation of the set of numbers.

In this case since the amount of water decreased in each tank is a constant value. The standard deviation does not change. So we know that Standard Deviation was same at the end of the year.

Statement 1 is sufficient.

Statement 2: In this case the amount decreased is 20% of each tank, which is a variable amount for each tank (depending on the water in each tank. Now if each tank had the same quantity of water, then decrease would be constant and the Standard Deviation would remain the same. But the tanks may also have different quantities of water, resulting in a different Standard Deviation at the end of the year. Since we do not have that information about the quantity of water in each tank, This Statement is not sufficient.

Wouldn't Statement 2 also be sufficient to answer the question.

Given that all volumes are reduced by the same percentage amount, the SD would also reduce by a particular amount and would never be the same as the starting standard deviation

Hey

If the old SD was 0, then new SD will also be 0 even if the it is reduced by 20%

But if old SD was x, then new SD will also change to 0.80*x

So Statement 2 is insufficient

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Re: The Department of Environmental Protection measured the volume of wate   [#permalink] 22 Apr 2018, 01:05
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